AUTHOR ""
TITLE "Exploring Time, Tense and Aspect in Natural Language Database Interfaces"
SUBJECT "Natural Language Processing, Volume 6"
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Exploring Time, Tense and Aspect in Natural Language Database Interfaces
Natural Language Processing Editor Prof. Ruslan Mitkov School of Humanities, Languages and Social Sciences University of Wolverhampton Stafford St. Wolverhampton WV1 1SB, United Kingdom Email:
[email protected] Advisory Board Christian Boitet (University of Grenoble) John Carroll (University of Sussex, Brighton) Eugene Charniak (Brown University, Providence) Eduard Hovy (Information Sciences Institute, USC) Richard Kittredge (University of Montreal) Geoffrey Leech (Lancaster University) Carlos Martin-Vide (Rovira i Virgili Un., Tarragona) Andrei Mikheev (University of Edinburgh) John Nerbonne (University of Groningen) Nicolas Nicolov (IBM, T. J. Watson Research Center) Kemal Oflazer (Sabanci University) Allan Ramsey (UMIST, Manchester) Monique Rolbert (Université de Marseille) Richard Sproat (AT&T Labs Research, Florham Park) Keh-Yih Su (Behaviour Design Corp.) Isabelle Trancoso (INESC, Lisbon) Benjamin Tsou (City University of Hong Kong) Jun-ichi Tsujii (University of Tokyo) Evelyne Tzoukermann (Bell Laboratories, Murray Hill) Yorick Wilks (University of Sheffield)
Volume 6 Exploring Time, Tense and Aspect in Natural Language Database Interfaces by Ion Androutsopoulos
Exploring Time, Tense and Aspect in Natural Language Database Interfaces
Ion Androutsopoulos Athens University of Economics and Business
John Benjamins Publishing Company Amsterdam/Philadelphia
8
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The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences – Permanence of Paper for Printed Library Materials, ansi z39.48-1984.
Library of Congress Cataloging-in-Publication Data Androutsopoulos, Ion Exploring Time, Tense and Aspect in Natural Language Database Interfaces / Ion Androutsopoulos. p. cm. (Natural Language Processing, issn 1567–8202 ; v. 6) Includes bibliographical references and index. 1. Grammar, Comparative and general--Temporal constructions--Data processing. 2. Grammar, Comparative and general--Verb--Data processing. 3. Computational linguistics. I. Title. II. Natural language processing (Amsterdam, Netherlands) ; v. 6. P294.5 A53 2002 415-dc21 isbn 9027249903 (Eur.) / 1588112691 (US) (Hb; alk. paper)
2002074690
© 2002 – John Benjamins B.V. No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher. John Benjamins Publishing Co. · P.O. Box 36224 · 1020 me Amsterdam · The Netherlands John Benjamins North America · P.O. Box 27519 · Philadelphia pa 19118-0519 · usa
Table of contents
Chapter 1 Introduction 1 1.1 What this book is about 1 1.2 Natural language interfaces to databases 5 1.3 Tense and aspect theories 9 1.4 Temporal logics 11 1.5 Temporal databases 13 1.6 Acknowledgements 17 Chapter 2 Linguistic data and an informal account 19 2.1 Introduction 19 2.2 Aspectual classes 20 2.3 The aspectual classes of this book 21 2.4 Criteria for classifying base verb forms 24 2.4.1 The simple present criterion 24 2.4.2 The point criterion 25 2.4.3 The imperfective paradox criterion 26 2.4.4 Other criteria 27 2.4.5 Classifying base verb forms in the airport domain 27 2.5 Verb forms 30 2.5.1 Simple present 30 2.5.2 Simple past 31 2.5.3 Progressive forms 32 2.5.4 Present perfect 36 2.5.5 Past perfect 38 2.6 Temporal verbs 39 2.7 Temporal nouns 40 2.8 Temporal adjectives 41 2.9 Temporal adverbials 41 2.9.1 Punctual adverbials 41
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2.10
2.11 2.12 2.13 2.14
2.9.2 Period adverbials 46 2.9.3 Duration adverbials introduced by ‘for’ 50 2.9.4 Duration adverbials introduced by ‘in’ 53 2.9.5 Other temporal adverbials 55 Temporal subordinate clauses 55 2.10.1 Clauses introduced by ‘while’ 55 2.10.2 Clauses introduced by ‘before’ and ‘after’ 58 2.10.3 Other temporal subordinate clauses 62 2.10.4 Tense coordination 63 Noun phrases and temporal reference 63 Temporal anaphora 65 Phenomena that will not be considered 67 Summary 69
Chapter 3 The TOP meaning representation language 71 3.1 Introduction 71 3.2 The syntax of TOP 72 3.3 TOP’s temporal ontology 77 3.4 TOP model 78 3.5 Variable assignment 80 3.6 Denotation of a TOP expression 80 3.7 The Pres operator 84 3.8 The Past operator 86 3.9 Progressives, non-progressives and the Culm operator 87 3.10 The At, Before and After operators 91 3.11 The Fills operator 95 3.12 The Begin and End operators 95 3.13 The Ntense operator 96 3.14 The For operator 98 3.15 The Perf operator 99 3.16 Occurrence identifiers 103 3.17 Tense anaphora and localisation time 105 3.18 Generic representatives of partitionings 106 3.19 Summary 106 Chapter 4 From English to TOP 109 4.1 Introduction 109
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4.2 HPSG basics 109 4.2.1 Lexical signs, lexical rules and sort hierarchy 110 4.2.2 Schemata and principles 112 4.3 Representing TOP yes/no formulae in HPSG 112 4.4 More on the subsorts of ind 115 4.5 Representing TOP quantifiers in HPSG 119 4.6 Extracting TOP formulae from HPSG signs 120 4.7 Verb forms 121 4.7.1 Single-word verb forms 121 4.7.2 Auxiliary verbs and multi-word verb forms 127 4.8 Predicative and non-predicative prepositions 133 4.8.1 Predicative prepositions 133 4.8.2 Non-predicative prepositions 135 4.9 Nouns 136 4.9.1 Non-predicative nouns 137 4.9.2 Predicative nouns 143 4.10 Adjectives 149 4.11 Temporal adverbials 153 4.11.1 Punctual adverbials 153 4.11.2 Period adverbials 159 4.11.3 Duration adverbials 160 4.12 Temporal complements of habituals 164 4.13 Fronted temporal modifiers 167 4.14 Temporal subordinate clauses 169 4.15 Interrogatives 170 4.16 Multiple temporal modifiers 174 4.17 Post-processing 178 4.18 Summary 181 Chapter 5 From TOP to TSQL2 183 5.1 Introduction 183 5.2 An introduction to TSQL2 183 5.2.1 The traditional relational model 183 5.2.2 TSQL2’s model of time 185 5.2.3 The BCDM version of the relational model 186 5.2.4 The TSQL2 language 189 5.3 Modifications to TSQL2 195 5.3.1 Referring to explicit attributes by number 195
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5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14
5.3.2 Additional partitioning units 196 5.3.3 Calendric relations 198 5.3.4 Other minor changes 200 Additional TSQL2 terminology 203 Adjustments in TOP and additional TOP terminology 206 Linking the TOP model to the database 207 The h functions 210 The TOP model in terms of database concepts 212 The h functions 213 Formulation of the translation problem 218 The translation rules 222 Optimising the generated TSQL2 code 231 Related work 233 Summary 235
Chapter 6 The prototype NLITDB 239 6.1 Introduction 239 6.2 Architecture of the prototype NLITDB 239 6.3 Implementation 241 6.4 Extensions for real-life applications 242 6.5 The airport database 245 6.6 Sample questions and output 247 6.7 Performance 265 6.8 Summary 265 Chapter 7 Related work and directions for further research 7.1 Introduction 267 7.2 Related work on NLITDBs 267 7.2.1 Moens 268 7.2.2 Clifford 269 7.2.3 Nelken 272 7.3 Directions for further research 278 7.4 Summary 279 References Index 293
283
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Appendix A TOP to TSQL2 translation rules 299 a.1 Translation rules for yes/no formulae 299 a.1.1 π(τ1 , . . . , τn ) 299 a.1.2 Culm[π(τ1 , . . . , τn )] 300 a.1.3 φ1 ∧ φ2 300 a.1.4 Pres[φ ] 301 a.1.5 Past[β, φ ] 301 a.1.6 Perf [β, φ ] 301 a.1.7 Ntense[β, φ ] 301 a.1.8 Ntense[now* , φ ] 302 a.1.9 For[σc , νqty , φ ] 302 a.1.10 Begin[φ ] 302 a.1.11 End[φ ] 302 a.1.12 At[κ, φ ] 302 a.1.13 Before[κ, φ ] 303 a.1.14 After[κ, φ ] 303 a.1.15 At[σg , β, φ ] 303 a.1.16 Before[σg , β, φ ] 303 a.1.17 After[σg , β, φ ] 303 a.1.18 At[σc , β, φ ] 304 a.1.19 Before[σc , β, φ ] 304 a.1.20 After[σc , β, φ ] 304 a.1.21 At[φ1 , φ2 ] 304 a.1.22 Before[φ1 , φ2 ] 305 a.1.23 After[φ1 , φ2 ] 305 a.2 Translation rules for wh-formulae 305 a.2.1 ?β1 . . . ?βk φ 306 a.2.2 ?mxl β1 ?β2 . . . ?βk φ 306
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Introduction
“No time like the present.”
. What this book is about For at least four decades, a very significant amount of work in artificial intelligence and computational linguistics has been devoted to natural language interaction, i.e., creating computer systems that allow their users to formulate requests in natural language, and systems that generate automatically appropriate natural language responses (Androutsopoulos & Aretoulaki 2002; Reiter & Dale 2000). One form of natural language interaction that has been studied extensively, and which is also the focus of this book, is database querying, where the term natural language interface is often used (Perrault & Grosz 1988; Copestake & Sparck Jones 1990; Androutsopoulos, Ritchie, & Thanisch 1995b; Androutsopoulos & Ritchie 2000). Natural language interfaces to databases (nlidbs) allow their users to retrieve information from an underlying database by submitting natural language queries, as illustrated in the following dialogue, where ‘U:’ and ‘S:’ mark user requests and system responses, respectively. U: S: U: S:
Which engineers work in the sales department? J.Adams, T.Smith. What are their salaries? J.Adams 2400 T.Smith 1800 U: What is the average salary in the sales department? S: 2250. The interaction may, in general, be in either spoken or written form, although this book considers only the latter; i.e., it will be assumed that the user types on a keyboard. This sidesteps speech recognition and synthesis (Jelinek 1997;
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Dutoit 1997; Gibbon, Moore, & Winski 1997; Hirschberg, Kamm, & Walker 1997; Bernsen, Dybkjaer, & Dybkjaer 1998). One of the limitations of existing nlidbs is that they were designed mainly to handle questions that refer to the present, as in the dialogue above or (1.1)– (1.3), and they do not support adequately the mechanisms that natural language employs to express time. For example, very few, if any, temporal adverbials (e.g., in 1991, after 5:00 pm) and verb forms (simple past, past continuous, past perfect, etc.) are typically supported, and their semantics are usually over-simplified or ignored. (1.1) What is the salary of each engineer? (1.2) Who is at site 4? (1.3) Which generators are in operation?
Database researchers have been exploring temporal database systems. These are intended to store and manipulate in a principled manner information not only about the present, but also about the past and future (Tansel et al. 1993; Jensen et al. 1998; Wu, Jajodia, & Wang 1998; Snodgrass 2000). When interfacing to temporal databases, it becomes crucial for nlidbs to interpret correctly the temporal mechanisms of natural language, which in questions like (1.4)–(1.6) include verb tenses, temporal adverbials, and temporal subordinate clauses. (1.4) What was the salary of each engineer while ScotCorp was building bridge 5? (1.5) Did anybody leave site 4 before the chief engineer had inspected the control room? (1.6) Which systems did the chief engineer inspect on Monday after the auxiliary generator was in operation?
Supporting the notion of time in nlidbs is a complex issue, as it requires ideas from three different time-related disciplines to be combined: linguistic theories of time, often referred to as tense and aspect theories (Comrie 1976; Comrie 1985; Smith 1997), temporal logics (van Benthem 1991; Gabbay, Hodkinson, & Reynolds 1994; Gabbay, Reynolds, & Finger 2000), and temporal databases. This point is easier to understand by considering Figure 1.1, which shows a simplified form of the architecture that many modern nlidbs adopt. As shown in Figure 1.1, the natural language question is first processed by a linguistic front-end. This analyses syntactically and semantically the question, and maps it to an expression of an intermediate meaning representation language, typically some kind of logic. The meaning representation expression captures formally what the system understands to be the meaning of the nat-
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Introduction natural language question
DB query linguistic front–end intermediate generator database language meaning expression representation
DBMS
results
Figure 1.1 Simplified NLIDB architecture
ural language question. The expression is then translated into a database language, usually sql (Melton & Simon 1993; Melton, Simon, & Gray 2001), that is supported by the underlying database management system (dbms); the latter is the part of the database system that manipulates the information in the database. Unlike the intermediate meaning representation, the database language expression specifies what information needs to be retrieved in terms of particular database constructs (e.g., rows and columns of tables in the database). The dbms retrieves this information by evaluating the database language expression, and the obtained information is reported back to the user. A response generator may also be involved, to convert the information to a form that is easier for the user to read; for simplicity, however, we will ignore response generation in the largest part of this book. The architecture of Figure 1.1 has proven to have several advantages (Androutsopoulos, Ritchie, & Thanisch 1995b; Androutsopoulos & Ritchie 2000); for example, the linguistic front-end is shielded from database-level issues, and it can be reused with dbmss that support different database languages. To support the notion of time in nlidbs, then, one first needs a concrete understanding of the variety, syntax, and semantics of the temporal mechanisms in natural language. The discussion in this book is limited to English. Ideas from linguistic theories of time can be drawn at this point, though one has to focus on ideas that are relevant to nlidb questions, as opposed, for example, to temporal phenomena that occur in longer event-reporting texts. A formally defined intermediate meaning representation language is also needed to represent the time-sensitive semantics of the questions; this is where ideas from temporal logics can be exploited. Furthermore, the meaning representation language must facilitate the mapping from natural language to formal representation; for example, by providing facilities that allow the semantic contribution of each temporal mechanism of natural language to be captured easily. Finally, an algorithm is needed to translate automatically from the meaning representation language to a temporal database language. The algorithm must be provably correct, in the sense that the database language expressions must preserve the semantics of the original meaning representations.
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Although there is a wealth of ideas in linguistic theories of time, temporal logics, and temporal databases, combining ideas from the three areas is not always straightforward. For example, it is often unclear how the semantics of linguistic theories of time can be expressed in formal meaning representation languages; and although numerous forms of temporal logic have been proposed, very few systematic mappings from natural language to expressions of those logics exist. Furthermore, there may be components in the temporal ontologies of linguistic theories or meaning representation languages that have no counterparts in temporal database models. The goal of this book is to explore how ideas from the three areas can be combined and refined, for the purposes of database querying, in order to produce a theoretical framework that will serve both as a starting point for developers of natural language interfaces to temporal databases (nlitdbs) and as a basis for further research. More specifically, Chapter 2 explores temporal linguistic phenomena that are likely to appear in English questions to nlitdbs. Drawing on existing tense and aspect theories, it formulates an account for many of these phenomena that is simple enough to be embodied in practical nlitdbs. Exploiting ideas from temporal logics, Chapter 3 then defines a temporal meaning representation language, called top, which is used to represent the semantics of the English questions. Chapter 4 shows how hpsg grammars (Pollard & Sag 1994) can be enhanced to incorporate the tense and aspect account of this book, and to map a wide range of English questions involving time to appropriate top expressions. Chapter 5 then presents a provably correct mapping that translates top expressions to appropriate tsql2 queries (Snodgrass 1995), tsql2 being a temporal extension of sql. This way a theoretical framework that establishes a sound route from English questions involving time to a temporal database language is constructed. To demonstrate that the framework is workable, it was used to implement a prototype nlitdb using ale (Carpenter 1992; Carpenter & Penn 2001) and Prolog. The prototype is freely available, and Chapter 6 provides more information about it. Finally, Chapter 7 compares the approach of this book to other attempts to build nlitdbs, and proposes directions for further research. This book is a revised version of the author’s PhD thesis (Androutsopoulos 1996). The reader will be pointed to the thesis for some mundane details, mostly parts of large proofs, that have not been included in the book. A summary of the thesis has also been published (Androutsopoulos, Ritchie, & Thanisch 1998). Like any natural language, English possesses a very large variety of temporal mechanisms, and it would be impossible for a book to consider how all of
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them can be supported in nlitdbs. Hence, this book focuses on a rich sample of English temporal mechanisms, paying particular attention to the description of the sample’s boundaries, and providing additional information to help the reader form a clear picture of what lies beyond them. Despite this limitation, the book should prove valuable to both people wishing to develop nlitdbs for practical applications, and those who plan further research, as it is essentially the first in-depth exploration of the time-related issues that arise in nlitdbs, from the linguistic level down to the database. The remainder of this chapter provides additional information on natural language interfaces, tense and aspect theories, temporal logics, and temporal databases, to help the reader obtain a clearer view of the book’s subject before moving on to the main discussion in following chapters. The book assumes that the reader has a solid background in symbolic approaches to natural language processing and computational linguistics, including unification-based grammars and formal semantics. Readers who do not have this background are advised to consult other introductory texts first (Shieber 1986; Gazdar & Mellish 1989; Allen 1995; Cole et al. 1997; Dale, Moisl, & Somers 2000; Jurafsky & Martin 2000; Mitkov 2002b).
. Natural language interfaces to databases Let us now examine in more detail the typical architecture of nlidbs, as shown in Figure 1.2; the top three modules correspond to the linguistic front-end of Figure 1.1. The user’s request first undergoes a preprocessing stage, which decomposes the input into tokens, i.e., words, punctuation marks, and other special symbols. The preprocessor also identifies and normalises expressions such as dates, times, and proper names. This is usually achieved by employing pattern-matching rules, and by consulting parts of the database or parts of the nlidb’s lexicon that contain proper names. For example, both October 12, 2001 and 12/10/2001 would be mapped to a common format; we will use dd/mm/yyyy as the common date format in this book. The preprocessed input is then parsed using a grammar, which in many systems includes rules that specify not only the possible syntactic structures, but also how these structures can be mapped to expressions of the meaning representation language. With a meaning representation language similar to first-order predicate logic, question (1.1) could be mapped to an expression like (1.7). The question marks are interrogative quantifiers; they mark the vari-
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Introduction natural language question
linguistic front-end preprocessing rules
preprocessor preprocessed input grammar
lexicon
parser meaning representation
discourse history
ontology
post-processor
fully resolved meaning representation translation rules
basic translation information
DB query generator
database language expression
domain–dependent information
DBMS
results
Figure 1.2 A typical NLIDB architecture in more detail
ables whose values are to be reported. To save space, throughout this book free variables are treated as existentially quantified. (1.7) ?x2 ?x3 engineer name(x1 , x2 ) ∧ salary of (x1 , x3 )
Expression (1.7) requires all the x2 and x3 to be reported, such that x2 is the name of an engineer x1 , and x3 is the salary of x1 . In questions like (1.4)– (1.6), the meaning representation language must provide appropriate facilities to capture the semantics of the temporal mechanisms of natural language; we will turn to this issue in later sections. The meaning representations that are generated at the end of the parsing are often underspecified; for example, they may not specify the exact entities that pronouns or other anaphoric expressions refer to. The underspecified
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parts of the meaning representations are resolved in a separate post-processing stage (Figure 1.2), which usually has access to broader information about the discourse; for example, in the form of a discourse history that records entities and facts that have been mentioned. In dialogue systems, where the emphasis is on engaging the users in dialogues until all the necessary information has been specified and interpretation problems have been solved, the post-processing is often one of the responsibilities of the dialogue manager (LuperFoy, Nijholt, & Veldhuijzen van Zanten 1996; Alexandersson 1999; Androutsopoulos & Aretoulaki 2002). This is a central coordinating module, which is also responsible for deciding when enough information is available to execute a user’s request, or when additional information must be requested from the user by generating an appropriate response. This book focuses on stand-alone questions, rather than questions that are parts of larger dialogues. Consequently, dialogue management issues will not be discussed, and the simple pipeline architecture of Figure 1.2 will suffice. We will also not consider techniques to resolve anaphoric expressions (Hirst 1981; Hobbs 1986; Barros & De Roeck 1994; Lappin & Leass 1994; Mitkov 2002a), although several temporal anaphora phenomena will be identified throughout the book, and preliminary ideas on how to handle some of them will be discussed. The parser and the post-processor often consult ontologies, mostly in the form of hierarchies that reflect the entity types of each application domain; for example, the hierarchy may show that a salesman is a type of employee, which is in turn a type of person. Additional restrictions on the possible relationships between entities of the various types are usually also present; for example, the manager of each employee must also be an employee, rather than, say, a product. Ontologies can be employed, among other things, to disambiguate user questions, as illustrated in (1.8). The intended meaning is (1.9); i.e., the holder of the licence is the employee. An nlidb, however, would also have to consider (1.10), where the licence is held by the branch. (1.8) List all the employees of Paris branches with driving licences. (1.9) ?x2 employee name(x1 , x2 ) ∧ branch name(x3 , x4 ) ∧ city name(x5, “Paris”) ∧ works at(x1 , x3 ) ∧ located in(x3 , x5 ) ∧ licence(x6 ) ∧ for driving(x6 ) ∧ has(x1 , x6 ) (1.10) ?x2 employee name(x1 , x2 ) ∧ branch name(x3 , x4 ) ∧ city name(x5, “Paris”) ∧ works at(x1 , x3 ) ∧ located in(x3 , x5 ) ∧ licence(x6 ) ∧ for driving(x6 ) ∧ has(x3 , x6 )
In order to reject (1.10), the ontology would need to contain a restriction stating that when the second argument of has(x, y) is a driving licence, the first one
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must be a person. The ontology’s hierarchy, then, would show that employees are persons, while branches are not, which would rule out (1.10). There will be opportunities to consider ontologies of this kind in greater detail in Chapter 4. The fully resolved meaning representation expressions that are generated at the end of the post-processing are subsequently translated into database language. This is often achieved using a recursive process. A ground mapping shows how basic meaning representation expressions relate to database constructs; for example, how predicates relate to database tables. Additional rules then specify how more complex meaning representation expressions can be translated, invoking recursively other rules to translate simpler subexpressions. This approach will be considered in more detail in Chapter 5. As already mentioned, a response generator may also be present. In most nlidbs, this is a rather simplistic module that formats the retrieved information to make it easier for the user to comprehend. More difficult is the generation of appropriate responses when the user’s requests carry false presuppositions or do not express literally what the user wants to do. In the first question below, the system detects the false presupposition that a flight named BA737 exists, and generates an appropriate warning. In the second question, it does not generate a simple affirmative response; it provides additional information, attempting to be more helpful. U: Does flight BA737 depart at 5:00 pm? S: Flight BA737 does not exist. U: Does any flight depart at 5:00 pm? S: Yes, UK160 and BA534. Responses of this kind are known as cooperative, and in the general case require a user model to represent the user’s goals and beliefs (Kobsa & Wahlster 1989). In many cases, however, relatively simple techniques suffice (Kaplan 1982). Although this book does not examine techniques to generate cooperative responses, several time-related phenomena that require responses of this kind will be identified. This implies that future work to add cooperative response capabilities to the theory of this book would be particularly useful; we will return to this point in Chapter 7. A different kind of responses that some nlidbs generate are paraphrases of the user’s requests that reflect the system’s understanding (De Roeck & Lowden 1986; Alshawi 1992; Alshawi et al. 1992). The paraphrases help the users detect cases where their requests have been misinterpreted. Paraphrases are also useful when ambiguities arise: unambiguous paraphrases of the original request can
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be generated, asking the user to select the paraphrase that corresponds to the intended reading. A significant amount of work on nlidbs has been devoted to portability, i.e., the ability to reuse nlidbs in different application domains; for example, with a database that holds information about train tickets, rather than the employees of a company. As shown in Figure 1.2, the core components of nlidbs are to a large extent domain-independent. Many of the resources that those components use, however, like the preprocessing rules, the lexicon, the ontology, and the mapping from basic meaning representation expressions to database constructs, are often domain-specific, and need to be configured whenever the nlidb is ported to a new application. The grammar of most nlidbs is designed to be reusable in a range of application domains, and, hence, it can be considered, to some extent, domainindependent. It should be noted, however, that every nlidb has a limited coverage of linguistic phenomena. Although Wizard of Oz experiments (Dahlbäck, Jönsson, & Ahrenberg 1993), where users interact with people pretending to be nlidbs, can be performed to study the questions of representative users and adjust the grammar accordingly, mismatches between the coverage of the grammar and the questions that actual users will submit are inevitable. Clarification dialogues and robust parsing techniques (Stallard & Bobrow 1993; Bates et al. 1994; Briscoe 1997) can be employed to recover from such mismatches; these issues, however, are beyond the scope of this book. An alternative approach, which will also not be discussed further, is to make the linguistic capabilities of the nlidb explicit to its users, in the form of a controlled language (Epstein 1985; claw 2000), possibly asking them to formulate their requests by selecting words from menus that reflect the available language constructs (Tennant et al. 1983).
. Tense and aspect theories In English, temporal information is conveyed by verb forms (e.g., simple past, past continuous, present perfect), nouns (e.g., beginning, predecessor, day), adjectives (earliest, next, annual), adverbs (yesterday, twice), prepositional phrases (at 5:00 pm, for two hours), and subordinate clauses (while tank 4 was empty), to mention just some of the available temporal mechanisms. A linguistic theory of time must account for the uses of these mechanisms; for example, it must specify the temporal semantic content of each verb form, and how temporal adverbials or temporal subordinate clauses affect the meanings of the overall
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sentences. The term tense and aspect theory is often used to refer to theories of this kind, although the precise meaning of ‘tense’ and ‘aspect’ varies from one theory to the other. Roughly speaking, in linguistics ‘tense’ usually refers to the ability of some language expressions to change form in order to convey information about the location of a situation in time (Comrie 1985); verbs are a typical example of such expressions in many languages. In contrast, ‘aspect’ does not refer to the location of a situation in time, but to how the situation is viewed by the speaker; e.g., whether or not it is conceived as being in progress, or as being an action or a state (Comrie 1985; Smith 1997). The sentences John sang and John was singing, then, are identical in terms of location in time (they both locate the situation in the past), but they differ in terms of aspect. Although in English tense is a property of verbs, which possibly extends to the syntactic constituents that contain them, this book is also concerned with other English mechanisms that specify location in time; for example, temporal adverbials. Following common practice, we will use the term ‘tense and aspect theory’ with a broad, and strictly speaking imprecise, sense to refer to a theoretical treatment of all the temporal mechanisms of a natural language. It is common in tense and aspect theories to classify natural language expressions or situations described by natural language expressions into aspectual classes; the German term Aktionsarten, kinds of action, is often used to refer to these classes. Many aspectual classifications are similar to Vendler’s taxonomy (1967), which distinguishes between state verbs, activity verbs, accomplishment verbs, and achievement verbs.1 For example, to run, as in John ran, is said to be an activity verb; to know, as in John knows the answer, is a state verb; to build, as in John built a house, is an accomplishment verb; and to find, as in Mary found the treasure, is an achievement verb. Vendler’s intuition seems to be that activity verbs, as in John ran, describe actions or changes in the world. In contrast, state verbs, as in John knows the answer, do not refer to any actions or changes. Accomplishment verbs are similar to activity verbs, in that they denote changes or actions. In the case of accomplishments, however, there is an inherent climax, a point that has to be reached for the action or change to be considered complete. In build a house, the climax is the point where the whole of the house has been built. If the building stops before this point has been reached, the building action is incomplete. In contrast, the action of the activity verb to run, as in John ran, with no object, does not seem to have any climax; the runner can stop at any time without the running being any more or less complete. If, however, to run is used with an object denoting a precise distance, as in to run a mile, then the action does have a cli-
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max: the point where the runner completes the distance. In this case, to run is an accomplishment verb. Finally, achievement verbs, like to find, describe instantaneous events. In Mary found the treasure, the actual finding is instantaneous; according to Vendler, the time when Mary was searching for the treasure is not part of the actual finding. In contrast, in John built a house, where the verb is an accomplishment, the actual building action may have lasted many years. The so-called imperfective paradox (Dowty 1977; Lascarides 1988; Kent 1993) is a well-known example of semantic differences related to aspectual classes. The paradox is that if the answer to a question like (1.11) is affirmative, then the answer to the non-progressive (1.12) must also be affirmative. In contrast, an affirmative answer to (1.13) does not necessarily imply an affirmative answer to (1.14), because John may have abandoned the repair before completing it. Hence, if an nlitdb generates an affirmative response to (1.11), there must be some mechanism to guarantee that the nlitdb’s answer to (1.12) will also be affirmative, unlike (1.13) and (1.14). (1.11) (1.12) (1.13) (1.14)
Was IBI ever advertising a new computer? Did IBI ever advertise a new computer? Was J. Adams ever repairing engine 2? Did J. Adams ever repair engine 2?
The difference between (1.11)–(1.12) and (1.13)–(1.14) can be accounted for by classifying to advertise and to repair as activity and accomplishment verbs, respectively, and by stipulating that the simple past of an accomplishment verb requires the climax to have been reached, while the simple past of an activity, as well as the past continuous of any verb, impose no such requirement. It will become clear in Chapter 2 that aspectual taxonomies pertain to the semantics of almost all of the English temporal mechanisms.
. Temporal logics Time is an important research topic in logic, and many formal languages have been proposed to express temporal information (van Benthem 1991; Gabbay, Hodkinson, & Reynolds 1994; Gabbay, Reynolds, & Finger 2000). One of the simplest approaches is to use the traditional first-order predicate logic, introducing time as an extra argument of each predicate. Question (1.15) could be represented as (1.16), where t is a time-denoting variable, ≺ stands for temporal precedence, for temporal inclusion, and now is a special term denoting the present moment.
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(1.15) Did tank 2 contain water (some time) on 1/10/1999? (1.16) ∃ t contain(tank2, water, t) ∧ t ≺ now ∧ t 1/10/1999
The answer to (1.15), then, is affirmative iff (1.16) evaluates to true, i.e., iff there is a time t, such that t precedes the present moment, t falls within 1/10/1999, and tank 2 contained water at t. (Throughout this book, ‘iff ’ will be used as a shorthand for ‘if and only if ’.) An alternative approach is to use temporal operators, like Prior’s P (past) and F (future) operators (Prior 1967). In that case, formulae are evaluated with respect to particular times. Assuming that φ is a formula, Pφ is true at a time t iff there is a time t , such that t precedes t, and φ is true at t . Similarly, Fφ is true at t iff there is a t , such that t follows t, and φ is true at t . Then, (1.17), (1.19), (1.21), and (1.23) could be represented as (1.18), (1.20), (1.22), and (1.24), respectively. (1.17) (1.18) (1.19) (1.20) (1.21) (1.22) (1.23) (1.24)
Tank 2 contains water. contain(tank2, water) Tank 2 contained water. P contain(tank2, water) Tank 2 will contain water. F contain(tank2, water) Tank 2 will have contained water. F P contain(tank2, water)
Additional operators can be introduced to capture the semantics of temporal adverbials, temporal subordinate clauses, etc. For example, an On operator could be introduced: if φ is a formula and κ specifies a day, then On[κ, φ] is true at a time t iff t falls within the day specified by κ, and φ is true at t. Then, (1.15) could be represented as (1.25). (1.25) P On[1/10/1999, contains(tank2, water)]
The intermediate meaning representation language of this book, top, uses temporal operators, mostly because they lead to more compact formulae, and make the semantic contribution of each linguistic mechanism easier to see. In fact, top stands for ‘language with Temporal OPerators’. Temporal operators have also been used by several other researchers (Dowty 1982; Lascarides 1988; Richards et al. 1989; Kent 1993; Crouch & Pulman 1993; Pratt & Bree 1995). Unlike logics designed to be used in systems that reason about what changes or remains the same over time, what can or will happen, what could or would have happened, or how newly acquired information fits within already known
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facts or assumptions (McCarthy & Hayes 1969; McDermott 1982; Kowalski & Sergot 1986; Allen 1983; Allen 1984; Vila 1994), top is not intended to be used in reasoning. No inference rules for top will be provided, and this is why this book avoids calling top a logic. It is only a formal language, designed to facilitate the systematic mapping of English questions involving time to formal expressions, a mapping most of the above mentioned logics are not concerned with. In the theory of this book, the answers to the English questions are not generated by performing inferencing in top, but by translating the top expressions to database language expressions, which are then evaluated by the underlying dbms. top will be defined in Chapter 3, where other ideas from temporal logics will also be discussed.
. Temporal databases In the relational model, currently the dominant database model, information is stored in relations (Ullman 1988). A relation can be thought of as a table, consisting of rows and columns. The tuples of the relation are, informally, the rows of the table, while the attributes of the relation are the table’s columns. The salaries relation below shows the present salaries of the current employees of a company. It has two attributes, employee and salary, and one tuple per employee. salaries employee J. Adams T. Smith ...
salary 21000 24000 ...
Whenever the salary of an employee is changed, or whenever an employee leaves the company, the corresponding tuple is modified or deleted. Hence, the database ‘forgets’ past facts, and does not contain enough information to answer questions like ‘What was the salary of T. Smith on 1/1/1992?’. It is certainly true that traditional database models and languages can, and have been, used to store temporal information. For example, two extra attributes, from and to, can be added to salaries to time-stamp its tuples, i.e., show when each employee had the corresponding salary, as in salaries2 below. The lack of special temporal support in traditional database models and languages, however, complicates time-related data manipulations. We may want, for example, to compute from salaries2 a new relation that shows the times when
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J. Adams and T. Smith had the same salary, along with their common salary, as in same salaries below. That is, for every tuple of J. Adams in salaries2, we need to check if the period specified by the from and to values of that tuple overlaps the period specified by the from and to values of a tuple for T. Smith with the same salary value. If they overlap, we need to compute the intersection of the two periods. This cannot be achieved easily in sql-92 (Melton & Simon 1993), what was until very recently the latest standard for sql, because sql-92 does not have any special commands to compute the intersection of two periods; in fact, it does not even have a period datatype. salaries2 employee J. Adams J. Adams J. Adams ... T. Smith T. Smith T. Smith ...
salary 17000 18000 21000 ... 17000 21000 24000 ...
from 1/1/1988 6/5/1990 10/8/1991 ... 1/1/1989 2/10/1990 24/5/1992 ...
same salaries salary from 17000 1/1/1989 21000 10/8/1991 ... ...
to 5/5/1990 9/8/1991 27/3/1993 ... 1/10/1990 23/5/1992 28/10/1994 ...
to 5/5/1990 23/5/1992 ...
As a further example, adding from and to attributes to every relation allows relations like rel1 and rel2 below to be formed. Although rel1 and rel2 contain different tuples, they can be seen as representing the same information, if the salary attribute shows the monthly salary of each person during the corresponding period. Checking if the two relations represent the same information is not easy in sql-92, because normalising them, i.e., turning them into rel3, an operation known as coalescing (Böhlen, Snodgrass, & Soo 1996), requires complex sql-92 statements. Additional examples of cases where special temporal support is particularly desirable in databases can be found in Snodgrass (2000). Numerous temporal versions of sql and the relational model have been proposed, that simplify the handling of time-sensitive information (McKenzie 1986; Stam & Snodgrass 1988; McKenzie & Snodgrass 1991; Soo 1991; Kline 1993; Tsotras & Kumar 1996; Wu, Jajodia, & Wang 1998). This book adopts
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tsql2 (Snodgrass 1995), a temporal extension of sql-92 that was designed by a committee of temporal database researchers and is a good representative of the various extensions that have been proposed. Chapter 5 presents a systematic and provably correct mapping from top to tsql2. rel1 employee G. Foot G. Foot G. Foot G. Foot
salary 17000 17000 18000 18000
from 1/1/1988 10/5/1988 10/5/1993 2/3/1994
to 9/5/1988 9/5/1993 1/3/1994 11/2/1995
rel2 employee G. Foot G. Foot G. Foot G. Foot
salary 17000 17000 17000 18000
from 1/1/1988 1/6/1989 11/8/1992 10/5/1993
to 31/5/1989 10/8/1992 9/5/1993 11/2/1995
rel3 employee G. Foot G. Foot
salary 17000 18000
from 1/1/1988 10/5/1993
to 9/5/1993 11/2/1995
At the time this book was being written, ansi recommendations on how to support time in the sql/Temporal part of the new sql:1999 standard (Melton, Simon, & Gray 2001), previously known as sql3, had been forwarded to iso (Snodgrass 2000). The recommendations are based on experience from tsql2 (Snodgrass et al. 1998), but they differ from tsql2 in many ways; the recommendations are closer to atsql (Böhlen, Jensen, & Snodgrass 2000), though again there are differences. Furthermore, to the best of the author’s knowledge, the recommendations are currently on hold, i.e., they will be considered by iso at a later point in time; hence, it is difficult to predict if they will be incorporated in sql:1999, and in exactly what form. Currently no major commercial dbms provides direct support for tsql2 or any of the other temporal extensions of sql. However, at least two add-ons for commercial dbmss exist, that support atsql or other closely related variants by translating their statements into equivalent, but often much more complex and hard to understand, statements of traditional sql. The author is aware of two add-ons of this kind: Tiger and timedb.2 The prototype nlitdb of Chapter 6
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is currently not linked to any of these add-ons, as this would require ironing the differences between the tsql2 version of this book and the temporal sql versions of the add-ons. Nevertheless, the top to tsql2 mapping of this book should serve as a useful precedent for researchers and developers wishing to work on nlitdbs with forthcoming temporal versions of sql. Similar mappings could be developed for other temporal flavours of sql as they become more standard in commercial dbmss. Temporal database researchers distinguish between valid time and transaction time. A temporal database may contain information about the history of the world it models, including predictions about the future. Valid time is the time-axis that underlies this history. The contents of the database, however, can be updated, in effect allowing the history of the world to be rewritten. Some temporal database systems support queries that refer to previously stored versions of the history. This establishes a second time dimension, transaction time, which allows queries to refer to past ‘beliefs’ of the database. In (1.26), then, on 2/1/1995 specifies the transaction time, while 1/1/1989 specifies the valid time. (1.26) According to what the database believed on 2/1/1995, what was the salary of J. Adams on 1/1/1989?
This book focuses on valid time, assuming that the English questions always refer to the current history in the database; i.e., the transaction time will always be the present. Furthermore, we will focus on questions about the past and the present, ignoring any predictions about the future that may be present in the database; this narrows the range of linguistic phenomena to be considered. As a further simplification, we will examine only questions, as opposed to requests to update the contents of the database (Davidson & Kaplan 1983). Assertions like (1.27) will be treated as yes/no questions; i.e., (1.27) will be treated in the same way as (1.28). (1.27) On 1/1/1999 the salary of T. Smith was 17000. (1.28) Was the salary of T. Smith 17000 on 1/1/1999?
Finally, although the tuples of the relations in the database may be updated, it will be assumed that the structure of the database remains unchanged; for example, we will not consider cases where attributes or relations are added or removed over time (McKenzie & Snodgrass 1990).
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. Acknowledgements The author wishes to thank Graeme Ritchie and Peter Thanisch, who supervised the work for his PhD thesis, on which this book is based, at the University of Edinburgh. The author is also grateful to the Greek State Scholarships Foundation (iky) for funding that work. The writing of this book was partly made possible by a post-doctoral scholarship from the Greek National Centre for Scientific Research (ncsr) ‘Demokritos’, and extensive support from the Software and Knowledge Engineering Laboratory of the Institute of Informatics and Telecommunications of ncsr. The ale grammar of the prototype nlitdb (Chapter 6) is based on previous ale encodings of hpsg fragments by Gerald Penn, Bob Carpenter, Suresh Manandhar, and Claire Grover; the author is indebted to all of them. Many thanks are also due to Chris Brew, who provided additional code for manipulating feature-structures in ale, and Jo Calder for his help with ale, pleuk, and hpsg grammars. The author is particularly indebted to Michael Böhlen, Rani Nelken, Maria Aretoulaki, and Stergos Afantenos, who provided comments on an earlier draft of this book.
Notes . According to Mourelatos (1978), a similar taxonomy was developed independently by Kenny (1963), who notes that his classification is similar to the distinction between kineseis and energiai introduced by Aristotle in Metaphysics, Θ.1048b, 18–36. . tiger was developed by a team directed by Michael Böhlen; see http://www.cs.auc.dk/tiger. timedb was developed by Andreas Steiner; see http://www.timeconsult.com.
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Chapter 2
Linguistic data and an informal account
“There is a time for everything.”
. Introduction This chapter explores how temporal information is conveyed in English, focusing on phenomena that are relevant to nlitdbs. Like any human language, English possesses a wealth of temporal mechanisms (Comrie 1976; Comrie 1985; Smith 1997). It would be impossible to consider all of them in this book. Hence, several English temporal mechanisms will be ignored, and simplifying assumptions will be introduced in some of the mechanisms that will be considered. One of the goals of this chapter is to help readers who are not familiar with tense and aspect phenomena appreciate their complexity. A second goal is to specify exactly which temporal phenomena this book will focus on. A wide range of English temporal mechanisms will be presented. From those, a subset containing mechanisms that seem both theoretically interesting and relevant to nlitdbs will be selected as the target linguistic coverage of this book. An informal account of the usage of the target mechanisms will also be provided; this will be formalised in subsequent chapters. The linguistic coverage of this book is intended to serve only as a starting point towards supporting the notion of time in nlitdbs. No attempt is made here to cover all the temporal linguistic mechanisms that an nlitdb might be confronted with. In a real-life nlitdb, the linguistic coverage of this book would have to be tailored to the range of applications that the nlitdb targets; for example, using Wizard of Oz experiments (Section 1.2). Unsupported mechanisms that are common in the target range of applications would have to be added, and the semantics of existing mechanisms might have to be adjusted to avoid, for example, readings that are uncommon in the targeted applications. Although the informal account of this chapter draws on existing analyses of tense and aspect, this book does not attempt to formulate a new or complete
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tense and aspect theory. The aim is more practical: to explore how ideas from existing tense and aspect treatments can be integrated into nlitdbs, in a way that leads to provably implementable systems.
. Aspectual classes Let us first examine more closely the notion of aspectual classes. As mentioned in Section 1.3, many tense and aspect treatments build upon Vendler’s taxonomy (Vendler 1967), that distinguishes between state verbs (John knows the answer), activity verbs (John ran), accomplishment verbs (John built a house), and achievement verbs (Mary found the treasure). Vendler proposes a number of linguistic tests to determine the aspectual classes of verbs. According to Vendler, activity and accomplishment verbs can appear in the progressive, as in (2.1) and (2.2), while state and achievement verbs cannot, as demonstrated in (2.3) and (2.4). (Throughout the book, asterisks will be used to mark ungrammatical sentences.) (2.1) (2.2) (2.3) (2.4)
John is running. John is building a house. *John is knowing the answer. *Mary is finding the treasure.
Activity verbs are said to combine felicitously with for adverbials specifying duration, as in (2.5), but sound odd with in duration adverbials, as in (2.6). (Question marks indicate sentences that sound odd, though not ungrammatical.) Accomplishment verbs, in contrast, combine felicitously with in adverbials, as in (2.7), and sound odd with for adverbials, as in (2.8). (2.5) (2.6) (2.7) (2.8)
John ran for two minutes. ?John ran in two minutes.
John built a house in two weeks. for two weeks.
?John built a house
Finally, according to Vendler, state verbs combine felicitously with for adverbials, as in (2.9), while achievement verbs sound odd, as demonstrated in (2.10). (2.9) John knew the answer for ten minutes (but then forgot it). (2.10) ?Mary found the treasure for two hours.
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The exact nature of the entities classified by Vendler is unclear. In most cases, Vendler’s wording suggests that his taxonomy classifies verbs. Some of his examples, however, like the fact that to run with no object is said to be an activity, while to run a mile is said to be an accomplishment, suggest that the natural language expressions being classified are not always verbs, but sometimes larger syntactic constituents, perhaps verb phrases. In other cases, Vendler’s arguments suggest that the entities being classified are not natural language expressions, but world situations denoted by natural language expressions. According to Vendler, ‘Are you smoking?’ asks about an activity, while ‘Do you smoke?’ asks about a state. In this case, the terms ‘activity’ and ‘state’ seem to refer to types of situations in the world, rather than types of natural language expressions. The first question probably asks if somebody is actually smoking at the present moment. The second one has a habitual meaning: it asks if somebody has the habit of smoking. Vendler concludes that habits “are also states in our sense”. Numerous variants of Vendler’s taxonomy have been proposed. These differ in the number of aspectual classes they assume, the names of the classes, the nature of the entities being classified, and the properties assigned to each class. For example, Vlach (1993) distinguishes four aspectual classes of sentences, and assumes that there is a parallel fourfold taxonomy of world situations. Moens (1987) distinguishes between ‘states’, ‘processes’, ‘culminated processes’, ‘culminations’, and ‘points’, commenting that his taxonomy does not classify real world situations, but ways people use to describe world situations. Parsons (1989) distinguishes three kinds of ‘eventualities’ (‘states’, ‘activities’, and ‘events’), treating eventualities as entities in the world. Lascarides (1988) classifies propositions, i.e., functions from time-periods to truth values, and distinguishes between ‘state’, ‘process’, and ‘event’ propositions.
. The aspectual classes of this book Four aspectual classes are employed in this book: states, activities, culminating activities, and points. Culminating activities and points correspond to Vendler’s ‘accomplishments’ and ‘achievements’, respectively. Similar terms have been used elsewhere (Moens 1987; Blackburn, Gardent, & de Rijke 1994). The four aspectual classes of this book correspond to ways of viewing world situations that people seem to use: a situation can be viewed as involving no change or action (state view), as an instantaneous change or action (point view), as a change or action with duration but no inherent climax (activity
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view), or as a change or action with both duration and inherent climax (culminating activity view). The climax is a point that has to be reached for the action or change to be considered complete, as in Section 1.3. Although there is evidence that people may distinguish between two subcases of point view, depending on whether or not the situation is seen as involving a change of state (Smith 1997), this distinction will be ignored in this book for the sake of simplicity. Determining which view the speaker has in mind is important to understand what the speaker means. For example, ‘Which tanks contained oil?’ is typically uttered with a state view. When an at temporal adverbial, like at 5:00 pm, is attached to a clause uttered with a state view, the speaker typically means that the situation of the clause simply holds at the time of the adverbial. There is normally no implication that the situation starts or stops at the time of the adverbial. For example, in ‘Which tanks contained oil at 5:00 pm?’ there is normally no implication that the tanks must have started or stopped containing oil at 5:00 pm. In contrast, ‘Who ran to the station?’ is typically uttered with a culminating activity view. In this case, an at adverbial usually specifies the time when the situation starts or is completed. For example, ‘Who ran to the station at 5:00 pm?’ probably asks who started to run to the station or reached it at 5:00 pm. Some linguistic markers seem to signal which view the speaker has in mind. For example, the progressive usually signals a state view. Unlike ‘Who ran to the station at 5:00 pm?’, ‘Who was running to the station at 5:00 pm?’ is typically uttered with a state view. In the progressive form, the running is simply ongoing at 5:00 pm; it does not start or finish at 5:00 pm. Often, however, there are no such explicit markers. The processes employed in those cases by hearers to determine the speaker’s view are not yet fully understood. In an nlitdb, however, where questions refer to a restricted application domain, reasonable guesses can be made by observing that in each domain, each verb tends to be associated mainly with one particular view. Certain agreements about how situations are to be viewed will also have been made during the design of the database. For example, the designers of the database may have decided that some situations will be modelled as instantaneous, a decision that users should be made aware of. Such agreements provide additional information about how the situations of the various verbs are viewed in each domain. More precisely, the following approach is adopted in this book. Whenever the nlitdb is configured for a new application domain, the base form of each verb is assigned to one of the four aspectual classes, using criteria to be discussed below. The criteria are intended to detect the view that is mainly associ-
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ated with each verb in the particular domain. Following Dowty (1986), Moens (1987), Vlach (1993), Smith (1997) and others, aspectual class is treated as a property of not only verbs, but also verb phrases, clauses, and sentences. Normally, all verb forms inherit the aspectual classes of the corresponding base forms. Verb phrases, clauses, or sentences normally inherit the aspectual classes of their main verb forms. Some linguistic mechanisms, however, like the progressive or some temporal adverbials, may cause the aspectual class of a verb form to differ from that of the base form, or the aspectual class of a verb phrase, clause, or sentence to differ from that of its main verb form. The aspectual class of each verb phrase, clause, or sentence is intended to reflect the view that the users of the nlitdb typically have in mind when using that expression in the particular domain. With verbs like to run, that typically involves a culminating activity view when used with an expression that specifies a particular destination or distance, as in to run to the station or to run five miles, but an activity view when used on its own, it will be assumed that there are two different homonymous verbs. One has a culminating activity base form, and requires a complement that specifies a particular destination or distance. The other has an activity base form, and does not accept such a complement. A similar distinction would be introduced in the case of verbs whose aspectual class depends on whether or not the verb’s object denotes a countable or mass entity, as in to drink a bottle of wine vs. to drink wine (Mourelatos 1978). Similarly, when a verb can be used in a domain with both habitual and non-habitual meanings, like to depart in (2.11) and (2.12), a distinction will be made between a homonym with a habitual meaning, and a homonym with a non-habitual meaning. The aspectual criteria that will be discussed below always classify the base forms of habitual homonyms as states. This agrees with Vendler, Vlach (1993), Moens and Steedman (1988), and Smith (1997), who all classify habituals as states. The aspectual classes of non-habitual homonyms will depend on the verbs and the application domain. (2.11) BA737 (habitually) departs from Gatwick. (2.12) BA737 (actually) departed from Gatwick five minutes ago.
Approaches that do not postulate homonyms are also possible. For example, one could treat to run as an activity, that is transformed into a culminating activity by a destination-denoting object, like to the station. Although perhaps less satisfactory from a theoretical point of view, the homonyms method leads to a more straightforward treatment in the hpsg grammar of Chapter 4, where the base form of each homonym will be mapped to a different lexical entry.
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Figure 2.1 Determining the aspectual class of a verb’s base form
In the rest of this book, the terms state verb, activity verb, culminating activity verb, and point verb refer to verbs whose base forms are classified as states, activities, culminating activities, or points, respectively.
. Criteria for classifying base verb forms Let us now turn to the criteria that determine the aspectual class of a verb’s base form in a particular application domain. Three criteria are employed, and they are applied in the order of Figure 2.1. .. The simple present criterion The first criterion, the simple present criterion, distinguishes state verbs from point, activity, and culminating activity verbs. The criterion states that if the simple present of a verb can be used in the particular domain in single-clause questions with non-future meanings, the verb is a state one; otherwise it is a point, activity, or culminating activity verb. For example, in domains where (2.13) and (2.14) are possible, to contain and to own are state verbs. (2.13) Does any tank contain oil? (2.14) Which employees own a car?
Some clarifications are needed at this point. First, the simple present sometimes refers to something that is scheduled to happen. For example, (2.15) could refer to a scheduled assembling; in that case, (2.15) is similar to (2.16). We will count readings of this kind as future ones. Hence, this use of (2.15) does not constitute evidence that to assemble is a state verb. (2.15) When does J. Adams assemble engine 5? (2.16) When will J. Adams assemble engine 5?
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Furthermore, in reporting contexts the simple present of verbs that we would not want to be classified as states can be used with non-future meanings. For example, in a context where the speaker reports events as they happen, (2.17) is possible. (2.17) J. Adams arrives. He moves the container. He fixes the engine.
This use of the simple present, however, is unlikely in nlitdb questions. Hence, (2.17) does not constitute evidence that to arrive, to move, and to fix are state verbs. The reader is reminded that when verbs have both habitual and nonhabitual meanings, a distinction is made between a habitual and a non-habitual homonym (Section 2.3). Ignoring future meanings, that do not count for the simple present criterion, (2.18) and (2.19) can only have habitual meanings; i.e., they can only be understood as involving the habitual homonyms of to land and to smoke. (2.18) Which flight lands on runway 2? (2.19) Does any doctor smoke?
Therefore, in domains where (2.18) and (2.19) are possible, the habitual homonyms of to land and to smoke are state verbs. (2.18) and (2.19) do not constitute evidence that the non-habitual homonyms of to land and to smoke are state verbs. .. The point criterion The second criterion, the point criterion, distinguishes point verbs from activity and culminating activity ones; state verbs will have already been separated by the simple present criterion (Figure 2.1). Some verbs denote situations that are modelled in the database as being always instantaneous. The point criterion states that if a verb denotes situations of this kind, its base form should be classified as point; otherwise, it should be classified as activity or culminating activity. Later on in this book, a hypothetical airport database will be considered. That database does not distinguish between the times at which a flight starts or stops entering an airspace sector. Entering a sector is modelled as instantaneous. Furthermore, to enter is only used to refer to flights entering sectors. Consequently, in that domain to enter is a point verb. If to enter were also used to refer to, for example, groups of passengers entering planes, and if situations of that kind were modelled in the database as non-instantaneous, we would
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distinguish between two homonyms of to enter: one used with flights entering sectors and one with passengers entering planes. The former would be classified as a point verb, while the latter would be classified as an activity or culminating activity verb. In applying the point criterion, one will often have to decide exactly what is or is not part of the situations that the verbs denote. For example, before classifying the non-habitual homonym of to depart, one has to decide exactly what is or is not part of departing. Is boarding part of departing, i.e., is a flight departing when it is boarding? Is taxiing to a runway part of departing? Or does departing include only the time at which the flight actually leaves the ground? The database that will be considered in later sections distinguishes between the time at which the boarding starts and the time when the flight leaves the ground. Hence, if a flight starts to depart when it starts to board and finishes departing when it leaves the ground, then the base form of to depart should not be classified as point, because the database does not model departures as instantaneous. If, however, departing starts when the front wheels of the aircraft leave the ground and finishes when the rear wheels leave the ground, the base form of to depart should be classified as point, because the particular database does not distinguish between the two times. In any case, the user should be made aware of what to depart is taken to mean. The point criterion is similar to observations made by Vendler (1967), Singh and Singh (1992), Vlach (1993), and others, that ‘achievement’ (point) verbs are understood as denoting instantaneous situations. .. The imperfective paradox criterion The third criterion, the imperfective paradox criterion, distinguishes activity from culminating activity verbs; state and point verbs will have been identified by the simple present and point criteria (Figure 2.1). This criterion is based on the imperfective paradox (Section 1.3). Assertions containing the past continuous and simple past of the verbs, like (2.20)–(2.23), are considered. The reader is reminded that assertions are treated as yes/no questions. If an affirmative answer to the past continuous assertion implies an affirmative answer to the simple past assertion, as in (2.20)–(2.21), the verb is an activity one; otherwise, as in (2.22)–(2.23), it is a culminating activity verb. (2.20) John was running. (2.21) John ran. (2.22) John was building a house.
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(2.23) John built a house.
As will be discussed in later sections, the past continuous sometimes has a future meaning. With this reading, (2.20) means that John was going to run, and an affirmative answer to (2.20) does not necessarily imply an affirmative answer to (2.21). When applying the imperfective paradox criterion, the past continuous must not have a future meaning. In various forms, the imperfective paradox criterion has been used by Vendler (1967), Vlach (1993), Kent (1993), and others. .. Other criteria The three criteria above are not the only ones that could be used. The behaviour of verbs when appearing in various forms or when combining with some temporal adverbials varies depending on their aspectual classes. Alternative criteria can be formulated by observing this behaviour. For example, some authors classify verbs, or situations denoted by verbs, by observing how easily they appear in progressive forms, or how easily they combine with for and in duration adverbials; these phenomena will be examined in later sections. In some cases, the person classifying the base forms may be confronted with verbs for which the three criteria of Sections 2.4.1–2.4.3 do not yield clear verdicts. In such cases, additional evidence for or against classifying a base verb form into a particular class can be found by referring to following sections, where the typical behaviour of each class is examined. .. Classifying base verb forms in the airport domain To illustrate the use of the three criteria, let us now consider in more detail the hypothetical airport database, borrowing some terminology from Sripada et al. (1994). The airport domain will be used in examples throughout this book. The airport database shows the times when flights arrived at, or departed from the airport, the times flights spent circling around the airport while waiting for permission to land, the runways they landed on or took off from, the gates where the flights boarded, etc. The database is occasionally queried using an nlitdb to determine the causes of accidents, and to collect data that are used to optimise the airport’s traffic-handling strategies. The airport’s airspace is divided into sectors. Flights approaching or leaving the airport cross the boundaries of sectors, each time leaving a sector and entering another one. The airport is very busy, and some of its runways may also be
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closed for maintenance. Hence, approaching flights are often instructed to circle around the airport until a runway becomes free. When a runway is freed, flights start to land. Landing involves following a specific procedure. In some cases, the pilot may abort the landing procedure before completing it. Otherwise, the flight lands on a runway, and it then taxies to a gate that is free. The moment at which the flight reaches the gate is considered to be the time when the flight arrived; reaching a location and arriving are modelled as instantaneous. Normally (habitually) each flight arrives at the same gate and time every day. Due to traffic congestion, however, a flight may arrive at a gate or time other than its normal ones. Before taking off, each flight is serviced by a service company. This involves carrying out a specific set of tasks. Unless all tasks have been carried out, the service is incomplete. Each service company normally (habitually) services particular flights. Sometimes, however, a company may be asked to service a flight that it does not normally service. After being serviced, a flight may be inspected. Apart from flights, inspectors also inspect gates and runways. In all cases, there are particular tasks to be carried out for the inspections to be considered complete. Shortly before taking off, flights start to board. Unless all the passengers that have checked in enter the aircraft, the boarding is not complete, and the flight cannot depart. There are special arrangements for cases where passengers are too late. The flight then leaves the gate, and that moment is considered to be the time at which the flight departed; leaving a location and departing are modelled as instantaneous. Normally (habitually) each flight departs from the same gate at the same time every day. Sometimes, however, flights depart from gates or at times other than their normal ones. After leaving its gate, a flight may be told to queue for a particular runway, until that runway is freed. When the runway is free, the flight starts to take off, which involves following a specific procedure. As with landings, the pilot may abort the taking off procedure before completing it. The database also records the status of parts of the airport’s emergency system. There are, for example, emergency tanks used by the fire-brigade. Some of those may contain water, others may contain foam, and others may be empty for maintenance. Table 2.1 shows some of the verbs that are used in the airport domain. The verbs to depart, to arrive, and to service are used with both habitual and nonhabitual meanings. Ignoring future meanings, questions (2.24) and (2.26) have habitual meanings, while in (2.25) and (2.27) the verbs are probably used with
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Table 2.1 Verbs in the airport domain state verbs
activity verbs
culm. activity verbs
point verbs
service (habitually) arrive (habitually) depart (habitually) contain be (non-auxiliary)
circle taxi (no destination) queue
land take off service (actually) inspect board taxi (to destination)
cross, enter become reach, leave start, begin stop, finish arrive (actually) depart (actually)
their non-habitual meanings. Following Section 2.3, we distinguish between habitual and non-habitual homonyms of to depart, to arrive, and to service. (2.24) (2.25) (2.26) (2.27)
Which flights depart/arrive at 8:00 am? Which flight departed/arrived at 8:00 am yesterday? Which company services BA737? Which company serviced BA737 yesterday?
Similarly, two homonyms of to taxi are assumed, one that requires a complement denoting a destination, as in BA737 was taxiing to gate 2, and one that admits no such complement, as in BA737 was taxiing. The simple present criterion and sentences like (2.28), (2.29), (2.24), and (2.26) imply that the non-auxiliary to be, to contain, and the habitual to depart, to arrive, and to service are state verbs. (2.28) Which gates are free? (2.29) Does any tank contain foam?
All the other verbs of Table 2.1 are not state verbs. For example, excluding habitual and future meanings, (2.30)–(2.32) sound unlikely or odd in the airport domain. (2.33)–(2.35) would be used instead. (2.30) (2.31) (2.32) (2.33) (2.34) (2.35)
?Which flights circle? ?Which flight
taxies to gate 2? departs? Which flights are circling? Which flight is taxiing to gate 2? Which flight is departing?
?Which flight
The verbs in the rightmost column of Table 2.1 denote situations that are modelled as instantaneous in the airport’s database. Consequently, by the point criterion, they are all point verbs. In contrast, the situations of the verbs in the
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two middle columns are not modelled as instantaneous. Therefore, those are activity or culminating activity verbs. In the airport domain, a sentence like (2.37) means that BA737 spent some time circling around the airport. It does not imply that BA737 completed any circle around the airport. Hence, an affirmative answer to (2.36) implies an affirmative answer to (2.37). By the imperfective paradox criterion, then, to circle is an activity verb. (2.36) BA737 was circling. (2.37) BA737 circled.
Similar assertions and the imperfective paradox criterion imply that to taxi without a destination and to queue are also activity verbs. In contrast, the verbs in the third column of Table 2.1 are culminating activity verbs. For example, in the airport domain an affirmative answer to (2.38) does not imply an affirmative answer to (2.39). J. Adams may have aborted the inspection before completing all the inspection tasks, in which case the inspection is incomplete. (2.38) J. Adams was inspecting runway 5. (2.39) J. Adams inspected runway 5.
. Verb forms Let us now explore the temporal role of the English verb forms. As already mentioned in Section 1.5, questions referring to the future are not examined in this book. Hence, future verb forms, like the simple future and future perfect, as well as future meanings of other forms, like the scheduled-to-happen meaning of the simple present (Section 2.4.1), will not be considered. To simplify the linguistic data further, the present perfect continuous and the past perfect continuous, as in J. Adams has/had been inspecting BA737, will also not be considered; these forms combine complexities from both progressive and perfect forms. This leaves six finite verb forms to be discussed: simple present, simple past, present continuous, past continuous, present perfect, and past perfect. .. Simple present In the linguistic coverage of this book, the simple present can be used only with state verbs to refer to a situation that holds at the present, as in (2.40) and (2.41). We will examine below the rationale behind this statement.
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(2.40) Which runways are closed? (2.41) Does any tank contain water?
Excluding future readings, (2.42) and (2.43) can be understood only with habitual meanings, i.e., as involving the habitual homonyms of to service and to depart. These are state verbs, unlike the non-habitual homonyms, which are culminating activity and point verbs, respectively (Table 2.1). This is consistent with the statement that the simple present can only be used with state verbs. (2.42) Which company services BA737? (2.43) Which flights depart from gate 2?
In the airport domain, to circle is an activity verb; there is no state habitual homonym. Hence, not allowing the simple present to be used with non-state verbs rejects (2.44). This is reasonable, because (2.44) can be understood only with a habitual meaning, which is not available in the airport domain. (2.44) ?Does BA737 circle?
Instead of simply rejecting (2.44), a cooperative nlitdb would inform the user that no habitual meaning of to circle is available, suggesting the rephrase of (2.45). As already mentioned in Section 1.2, however, mechanisms to generate cooperative responses are not considered in this book. (2.45) Is BA737 circling?
One could point out that the simple present can be used with non-state verbs to describe events as they happen (Section 2.4.1), or with a historic meaning (‘In 1673 a fire destroys the palace.’). These uses, however, are extremely unlikely in nlitdb questions. Hence, the statement that the simple present can be used only with state verbs remains valid for the purposes of this book. .. Simple past Unlike the simple present, the simple past can be used with verbs from all four classes, as in (2.46)–(2.51). (2.46) (2.47) (2.48) (2.49) (2.50) (2.51)
Which tanks contained water on 1/1/1999? Did BA737 circle on 1/1/1999? Which flights (actually) departed from gate 2 on 1/1/1999? Which flights (habitually) departed from gate 2 in 1999? Which company (actually) serviced BA737 yesterday? Which company (habitually) serviced BA737 last year?
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Questions (2.48)–(2.51) show that both the habitual and non-habitual homonyms of verbs like to depart or to service are generally possible in the simple past. (2.52) is ambiguous. It may refer either to flights that actually departed, perhaps only once, from gate 2 in 1999, or to flights that normally, habitually, departed from gate 2 in 1999. (2.52) Which flights departed from gate 2 in 1999?
The simple past of culminating activity verbs normally implies that the situation of the verb reached its climax. For example, in (2.53) the service must have been completed, and in (2.54) BA737 must have reached gate 2 for the answer to be affirmative. (2.53) Did Airserve service BA737? (2.54) Did BA737 taxi to gate 2?
Although strictly speaking correct, a simple negative answer to a question like (2.54) may in practice be unsatisfactory, if, for example, BA737 was taxiing to gate 2, but never reached it. (2.55) would be a much more appropriate answer. Again, a mechanism for cooperative responses is needed to generate answers like (2.55), but this book does not consider such mechanisms. (2.55) BA737 was taxiing to gate 2, but never reached it.
Finally, it should be noted that the simple past often has an anaphoric nature. For example, (2.53) is probably not asking if Airserve serviced BA737 at any time in the past. (2.53) would typically be used with a particular time in mind, perhaps the present day, to ask if Airserve serviced BA737 during that time. A temporal anaphora resolution mechanism is needed to determine the time that the speaker has in mind. Such mechanisms, however, are not considered in this book (Section 1.2), and (2.53) will be taken to refer to any past time. The same approach is adopted with all other verb forms that refer to past situations. Issues related to temporal anaphora will be considered further in Section 2.12. .. Progressive forms Let us now turn to the progressive verb forms that will be considered in this book: the present continuous and past continuous. The reader is reminded that future meanings are not considered. This means that, for example, the case where (2.56) has a reading similar to that of (2.57) will be ignored. (2.56) Who is/was inspecting BA737?
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(2.57) Who will/would inspect BA737?
In the following paragraphs, we will examine in turn the progressive forms of activity and culminating activity verbs, point verbs, and state verbs.
Activity and culminating activity verbs in progressive forms. The present and past continuous can be used with activity and culminating activity verbs to refer to a situation that is or was in progress, as in (2.58)–(2.59) in the airport domain. (2.58) Are/Were any flights circling? (2.59) Is/Was BA737 taxiing to gate 2?
In the case of culminating activity verbs, there is no requirement for the climax to be reached at any time. The past continuous version of (2.59), for example, does not require BA737 to have reached gate 2 (cf. (2.54)).
Point verbs in progressive forms. With point verbs, the use of progressive forms is often an indication that the user is unaware that the situation of the verb is modelled in the database as instantaneous. In the airport domain, for example, the non-habitual to depart is a point verb, and departing is taken to include only the time-point where the flight leaves its gate. In contrast, (2.60) seems to be referring to a situation with duration; a user who is aware that departures are modelled as instantaneous would normally use (2.61) instead. Similarly, (2.62) seems to be carrying the assumption that departures are not instantaneous, so that the speaker can talk while BA737 is departing. (2.60) BA737 was departing. (2.61) BA737 departed. (2.62) BA737 is departing.
In sentences like (2.60)–(2.62), a cooperative nlitdb would warn the user that departures are modelled as instantaneous. In the absence of mechanisms to generate cooperative responses, the framework of this book silently accepts the progressive forms of point verbs as referring to the instantaneous situations of the verbs. The past continuous simply places the instantaneous situation of the verb in the past, as when the simple past is used; for example, (2.60) is taken to have the same meaning as (2.61). The present continuous asserts that the instantaneous situation of the verb occurs at the present time-point. As will be discussed in Chapter 5, in practice the database may model time-points as corresponding to minutes or even whole days. Hence, obtaining an affir-
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mative answer to a yes/no question like (2.62) is less unlikely than the reader might think. It is worth noting that people often seem to employ conceptual mechanisms that allow them to add duration to situations that would normally be thought of as instantaneous (Moens 1987). When confronted, for example, with a past continuous sentence like (2.63), which seems to require the normally instantaneous reaching to be seen as having duration, people often attach a preparatory process to the instantaneous situation of the verb; in (2.63), this could be the covering of a short remaining distance up to the gate. The progressive is then taken to assert that the preparatory process was in progress. (2.63) At 5:00 pm BA737 was reaching gate 2.
In other cases, an iterative reading may be employed in order to add duration to the situation of the verb. In (2.64), for example, the most natural reading is that John is banging his hand repeatedly. (2.64) John is banging his hand on the table.
Figuring out, however, exactly which preparatory process should be attached to an instantaneous situation, or exactly when an iterative reading is licensed is a difficult task for an nlitdb. Hence, the theoretical framework of this book provides no mechanisms for adding preparatory processes or for generating iterative readings.
State verbs in progressive forms. It has often been observed that state verbs are not normally used in progressive forms (cf. Vendler’s tests in Section 2.2). For example, (2.65) and (2.67) are easily rejected by most native English speakers. It is assumed here that to own and to consist would be classified as state verbs, on the basis that simple present questions like (2.66) and (2.68) are possible. (2.65) (2.66) (2.67) (2.68)
*Who is owning five cars? Who owns five cars? *Which engine is consisting of 34 parts? Which engine consists of 34 parts?
The claim that state verbs do not appear in the progressive is challenged by sentences like (2.69), from Smith (1986); Kent (1993) and Vlach (1993) provide similar examples. (2.69) shows that the non-auxiliary to be, which is typically classified as a state verb, can be used in the progressive. (2.69) My daughter is being very naughty.
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Furthermore, some native English speakers find (2.70) and (2.71) acceptable, though they would use the non-progressive forms instead. It is assumed here that to border would be classified as state verb, on the basis that (2.72) is possible. (2.70) Tank 4 was containing water when the bomb exploded. (2.71) Which countries were bordering France in 1937? (2.72) Which countries border France?
Not allowing progressive forms of state verbs also seems problematic in questions like (2.73), that has a reading very similar to the habitual reading of (2.74). (2.73) Which company was servicing BA737 in 1999? (2.74) Which company serviced (habitually) BA737 in 1999?
The reader is reminded that in the airport domain a distinction is made between the habitual and non-habitual homonym of to service. The habitual homonym is a state verb, while the non-habitual one is a culminating activity verb. If progressive forms of state verbs are not allowed, then only the nonhabitual homonym (actually servicing) is possible in (2.73). This does not account for the apparently habitual meaning of (2.73). One could argue that the reading of (2.73) is not really habitual, but iterative: servicing many times, as opposed to having a servicing habit. In sentences like (2.73)–(2.74), however, the difference between habitual and iterative meaning is hard to define. Given that it seems harmless to accept sentences like (2.65) and (2.67) in an nlitdb, the theoretical framework of this book allows state verbs to be used in progressive forms, with the same meanings as the corresponding nonprogressive forms. This causes (2.73) to receive two readings: one involving the habitual to service (servicing habitually in 1999), and one involving the nonhabitual to service (actually servicing at some time in 1999); the latter reading is more likely without the adverbial. (2.65) and (2.67) are treated as equivalent to (2.66) and (2.68), respectively.
Aspectual shift of progressives. The progressive will be taken to cause an aspectual shift from activities and culminating activities to states; no shift is necessary in the case of points. In the airport domain, for example, although the base form of to inspect is a culminating activity, was inspecting will be a state. The shift will allow us to account for the meaning of progressives when they combine with temporal adverbials; this will be discussed further in Section 2.9.
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In various forms, similar shifts have been employed by Dowty (1986), Moens (1987), Vlach (1993), Kent (1993), and others. .. Present perfect Like the simple past, the present perfect can be used with verbs of all four aspectual classes to refer to past situations, as in (2.75)–(2.79). With culminating activity verbs, the situation must have reached its climax; in (2.79), for example, the service must have been completed. (2.75) (2.76) (2.77) (2.78) (2.79)
Has BA737 (ever) been at gate 2? Which flights have circled today? Has BA737 reached gate 2? Which company has (habitually) serviced BA737 this year? Has Airserve (actually) serviced BA737?
Present perfect and present consequences. It has often been claimed that the English present perfect asserts that some consequence of the past situation holds at the present (Moens 1987; Vlach 1993; Blackburn, Gardent, & de Rijke 1994). For example, (2.80) seems to imply that there is a consequence of the fact that engine 5 caught fire that still holds. The consequence could be, for example, that engine 5 is still on fire, or that it was damaged by the fire and has not been repaired. In contrast, (2.81) does not seem to imply, at least not as strongly, that some consequence still holds. (2.80) Engine 5 has caught fire. (2.81) Engine 5 caught fire.
Although these claims are intuitively appealing, it is difficult to see how they could be used in an nlitdb. Perhaps in (2.82) the nlitdb should check not only that the landing was completed, but also that some consequence of the landing still holds. (2.82) Has BA737 landed?
It is unclear, however, what this consequence should be. Should the nlitdb check that the plane is still at the airport? Should it check that the passengers of BA737 are still at the airport? Furthermore, in the first case, should the answer be negative if the plane has departed since the landing? Given this uncertainty, the framework of this book does not require the past situation to have present consequences.
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A second, related point is that when the present perfect combines with for duration adverbials, there is often an implication that the past situation still holds at the present. This seems related to the claims that the past situation must have present consequences. For example, one reading of (2.83) is that J. Adams is still a manager. (An alternative reading is that J. Adams was simply a manager for two years, without the two years ending at the present moment.) In contrast, (2.84) carries no implication that J. Adams is still a manager; in fact, it seems to imply that he is no longer a manager. (2.83) J. Adams has been a manager for two years. (2.84) J. Adams was a manager for two years.
For simplicity, in the framework of this book the still-holding reading of sentences like (2.83) will be ignored, and (2.83) will be treated as having the same meaning as (2.84).
Present perfect and temporal adverbials. The present perfect does not combine felicitously with some temporal adverbials. For example, (2.85) and (2.88) sound unacceptable to most native English speakers; they would use (2.86) and (2.89) instead. In contrast, (2.87) and (2.90) are acceptable. (2.85) (2.86) (2.87) (2.88) (2.89) (2.90)
*Which flights have landed yesterday? Which flights landed yesterday? Which flights have landed today? *Which flights has J. Adams inspected last week? Which flights did J. Adams inspect last week? Which flights has J. Adams inspected this week?
Questions (2.85)–(2.90) suggest that the present perfect can be used only if the time of the adverbial contains not only the time where the past situation occurred, but also the speech time, the time when the sentence was uttered. Thomson and Martinet (1986:167) provide a similar account. (2.87) is felicitous, because today contains the speech time. In contrast, (2.85) is unacceptable, because yesterday cannot contain the speech time. The hypothesis, however, that the time of the adverbial must include the speech time does not account for the fact that (2.91) is acceptable by most native English speakers, especially if the ever is added, even if the question is not uttered on a Sunday. (2.91) Has J. Adams (ever) inspected BA737 on a Sunday?
Moens and Steedman (1988) also point out that a superstitious person could utter (2.92) on a day other than Friday the 13th.
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(2.92) They have married on Friday 13th!
One could attempt to formulate more elaborate restrictions, to predict exactly when temporal adverbials can be used with the present perfect. In the case of an nlitdb, however, it is difficult to see why this would be worth the effort, as opposed to simply accepting questions like (2.85) as equivalent to (2.86). The framework of this book adopts the latter approach. Given that the framework of this book does not associate present consequences with the present perfect, that the still-holding reading of sentences like (2.83) is not supported, and that questions like (2.85) are allowed, there is not much left to distinguish the present perfect from the simple past. Hence, for simplicity, in this book the present perfect will be treated as having the same meaning as the simple past. .. Past perfect The past perfect is often used to refer to a situation that occurred at some past time before some other past time. Following Reichenbach (1947), let us call the latter time the reference time. (2.93) and (2.94) have readings where at 5:00 pm specifies the reference time. In that case, (2.93) asks for flights that Airserve serviced before 5:00 pm, and (2.94) asks if BA737 was at gate 2 some time before 5:00 pm. (2.93) Which flights had Airserve serviced at 5:00 pm? (2.94) Had BA737 been at gate 2 at 5:00 pm?
With culminating activity verbs, the climax must have been reached before, or possibly at, the reference time. For example, in (2.93) the services must have been completed up to 5:00 pm. Perhaps some consequence of the past situation must still hold at the reference time. As with the present perfect, however, such consequential links will be ignored in this book. When the past perfect combines with temporal adverbials, it is often unclear if the adverbial is intended to specify the reference time or directly the time of the past situation. For example, (2.95) could mean that BA737 had already reached gate 2 at 5:00 pm, or that it reached it at 5:00 pm. In the latter case, (2.95) is similar to the simple past (2.96), except that (2.95) creates the impression of a longer distance between the time of the reaching and the speech time. (2.95) BA737 had reached gate 2 at 5:00 pm. (2.96) BA737 reached gate 2 at 5:00 pm. (2.97) BA737 had reached gate 2 by 5:00 pm.
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By adverbials are often used in practice to clarify that the adverbial specifies the reference time, as in (2.97) (cf. (2.95)). By adverbials, however, are not considered in this book. When the past perfect combines with for duration adverbials and a reference time is specified, there is often an implication that the past situation still held at the reference time. For example, (2.98) seems to imply that J. Adams was still a manager on 1/1/1999. As in the case of the present perfect, this implication will not be captured by the framework of this book. (2.98) J. Adams had been a manager for two years on 1/1/1999.
Aspectual shift of past perfect. The past perfect will be taken to trigger an aspectual shift from activities, culminating activities, and points to states. For example, the base form of to inspect is a culminating activity in the airport domain, but had inspected will be treated as a state. This shift will allow us to account for the behaviour of the past perfect when combining with temporal adverbials, and it seems to be a property of all perfect forms. However, since the present perfect is treated as having the same meaning as the simple past (Section 2.5.4), no such shift will be postulated in the case of the present perfect. Similar shifts have been employed by Moens (1987), Vlach (1993), and others.
. Temporal verbs Through their various forms, all verbs can convey temporal information. Some verbs, however, like to begin or to precede, are of a more inherently temporal nature. They differ from ordinary ones, like to build or to contain, in that they do not describe directly situations, but rather refer to situations introduced by other verbs or nouns; Passonneau (1988) makes a similar observation. In (2.99), for example, to begin refers to the situation of to build. The verbs to start, to end, to finish, to follow, to continue, and to happen all belong to this category of special temporal verbs. (2.99) They began to build terminal 9 in 1985.
Only four of these special verbs will be considered in this book: to start, to begin, to stop, and to finish. For simplicity, all four of them will be allowed to combine with state and activity verbs. It should be noted, however, that with state verbs to begin and to finish usually sound unnatural, as demonstrated in (2.100) and (2.101); and with activity verbs, as in (2.102), it could be argued that the use of
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to begin or to finish indicates that the speaker has a culminating activity view in mind, rather than an activity one. (2.100) ?Which tank began to contain water on 27/7/1999? (2.101) ?Which tank finished containing water on 27/7/1999? (2.102) Which flight began/finished circling at 5:00 pm?
When combining with culminating activity verbs, to start and to begin have the same meanings. The verbs to stop and to finish, however, differ: to finish requires the climax to be reached, while to stop requires the action or change to simply stop, possibly without being completed. For example, in (2.103) the service must have simply stopped, while in (2.104) it must have been completed. Nonhabitual readings are assumed here. (2.103) Which company stopped servicing BA737 at 5:00 pm? (2.104) Which company finished servicing BA737 at 5:00 pm?
With point verbs, like to enter and to leave in the airport domain, the use of to start, to begin, to stop, and to finish, as in (2.105) and (2.106), typically signals that the person submitting the question is unaware that the situation of the point verb is taken to be instantaneous. In such cases, the temporal verbs will be ignored, i.e., (2.105) and (2.106) will be treated as (2.107). (2.105) Which flight started to enter sector 2 at 5:00 pm? (2.106) Which flight finished leaving gate 2 at 5:00 pm? (2.107) Which flight entered sector 2 at 5:00 pm?
Ideally, an nlitdb would also warn the user that the temporal verb is ignored, and that the situation is modelled as instantaneous. This is another case where cooperative responses are necessary.
. Temporal nouns In a similar manner, some nouns have a special temporal nature. Nouns like development or inspection, for example, are similar to verbs, in that they introduce world situations that occur in time. The role of development in (2.108) is very similar to that of to develop in (2.109). (2.108) When did the development of masque start? (2.109) When did they start to develop masque?
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Other nouns, like predecessor and successor, indicate temporal order, or refer to start or end-points, like beginning or end. Finally, many nouns, as well as proper names, refer to time periods, points, or generally entities of the temporal ontology; e.g., minute, July, event. This book will consider only nouns like year, month, week, day, minute, and proper names like 1999, July, 1/1/1999, Monday, 3:05 pm. Temporal nouns of a more abstract nature, like period, point, interval, event, time, duration, nouns referring to start or end-points, nouns introducing situations, and nouns of temporal precedence will not be considered.
. Temporal adjectives There are also adjectives of a special temporal nature. Some refer to temporal order, like current, previous, earlier. Some refer to durations; e.g., brief, long. Others, like annual or daily, specify frequencies. Adjectives of this kind are not examined in this book, with the exception of current, which is supported to illustrate some issues related to temporal anaphora.
. Temporal adverbials We now turn to adverbials that convey temporal information. This book considers four types of temporal adverbials: punctual adverbials, period adverbials, and duration adverbials introduced by for and in. For each type, we will consider in turn the cases where the adverbials modify, i.e., attach to, expressions of the four aspectual classes: states, points, activities, and culminating activities. .. Punctual adverbials Some adverbials are understood as specifying time-points. Following Vlach (1993), the term punctual adverbials will be used to refer to them. In English, punctual adverbials are usually prepositional phrases introduced by at, as in at 5:00 pm or at the end of the inspection. In this book, only punctual adverbials consisting of at and clock-time expressions, like at 5:00 pm, will be considered.
Punctual adverbials with states. When combining with state expressions, punctual adverbials specify a time where the situation of the state expression holds. There is usually no implication that the situation of the state starts or
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stops at the time of the adverbial. (2.110), for example, asks if tank 5 was empty at 5:00 pm. There is no requirement that the tank must have started or stopped being empty at 5:00 pm. Similar comments apply to (2.111). (2.110) Was tank 5 empty at 5:00 pm? (2.111) Which flight was at gate 2 at 5:00 pm?
In other words, punctual adverbials normally have an interjacent meaning with states, not an inchoative (start time of situation) or a terminal one (end time of situation). These terms are borrowed from Kent (1993), who explores the behaviour of at, for, and in adverbials, arriving at conclusions similar to the ones presented here. In narrative contexts, punctual adverbials combining with states sometimes have inchoative meanings. For example, the at 8:10 am in (2.112) most probably specifies the time when J. Adams arrived (started being) in Glasgow. In nlitdb questions, however, this inchoative meaning seems unlikely. For example, it seems unlikely that (2.113) would be used to enquire about persons that arrived in Glasgow at 8:10 am. Hence, for the purposes of this book, it seems reasonable to assume that punctual adverbials combining with states always have interjacent meanings. (2.112) J. Adams left Edinburgh early in the morning, and at 8:10 am he was in Glasgow. (2.113) Who was in Glasgow at 8:10 am?
Punctual adverbials with points. With point expressions, punctual adverbials specify the time where the instantaneous situation of the point expression takes place, as in (2.114) and (2.115). The reader is reminded that to enter and to reach are point verbs in the airport domain (Section 2.4.5). (2.114) Which flight entered sector 2 at 23:02? (2.115) Which flight reached gate 5 at 23:02?
Question (2.116) is ambiguous. It may involve the non-habitual homonym of to depart, which is a point verb in the airport domain; in that case, 5:00 pm is the time of the actual departure. Alternatively, it may involve the state habitual homonym, in which case 5:00 pm is the habitual departure time. In the latter case, at 5:00 pm will be treated as a prepositional phrase complement of the habitual to depart, not as a temporal adverbial. This reflects the fact that the at 5:00 pm does not specify a time when the habit holds, but it forms part of the
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description of the habit, i.e., it is used in a way very similar to how from gate 2 is used in (2.117). (2.116) Which flight departed at 5:00 pm? (2.117) Which flight departed (habitually) from gate 2 (last year)?
Punctual adverbials with activities. With activities, punctual adverbials usually have an inchoative meaning, but an interjacent one is also possible in some cases. (2.118), for example, could refer to a flight that either joined the queue of runway 2 at 5:00 pm or was simply in the queue at 5:00 pm. The reader is reminded that in the airport domain, to queue and to taxi without a destination are activity verbs. The inchoative meaning seems the preferred one in (2.118). It also seems the preferred one in (2.119), though an interjacent meaning is arguably also possible. The interjacent meaning is easier to accept in (2.120). (2.118) Which flight queued for runway 2 at 5:00 pm? (2.119) BA737 taxied at 5:00 pm. (2.120) Which flights circled at 5:00 pm?
With past progressive forms of activity verbs, punctual adverbials normally have only interjacent meanings. Compare, for example, (2.118) and (2.119) to (2.121) and (2.122). One would not normally use punctual adverbials with present continuous forms, since in that case the situation is known to take place at the present. (2.121) Which flight was queueing for runway 2 at 5:00 pm? (2.122) BA737 was taxiing at 5:00 pm.
Following the arrangements of Section 2.5.3, it will be assumed that the progressive triggers an aspectual shift from activities and culminating activities to states. Hence, although to queue is an activity verb in the airport domain, was queueing is a state expression. Along with the assumption that punctual adverbials have only interjacent meanings when combining with states, this accounts for the fact that (2.121) can only be understood with an interjacent meaning. Similar comments apply to (2.122).
Punctual adverbials with culminating activities. With culminating activities, punctual adverbials usually have inchoative or terminal meanings; when they have terminal meanings, they specify the time at which the climax was reached. In the airport domain, for example, to land, to taxi to a destination, and to inspect are culminating activity verbs. The terminal reading is the preferred
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one in (2.123). In (2.124) both readings seem possible, while in (2.125) the inchoative meaning seems the preferred one. (2.123) Which flight landed at 5:00 pm? (2.124) Which flight taxied to gate 4 at 5:00 pm? (2.125) Who inspected BA737 at 5:00 pm?
One could argue that in (2.123) the speaker does not have a culminating activity view in mind, but a point view, whereby the landing situation is seen as consisting of only the time-point at which the aircraft touches the ground. Indeed, as will be explained in following paragraphs, it will be assumed that punctual adverbials change the aspectual class of the expressions they modify to point. With culminating activities, this is achieved by forcing the modified expressions to refer to either the beginnings or the completions of the situations they would normally denote. In (2.123), the completion of the landing is conceptually more salient than its beginning, which is why the terminal reading is the preferred one. In (2.124) and (2.125), however, neither the beginning nor the completion is more salient, which is why the questions sound much more unclear than (2.123); in practice, a speaker would use temporal verbs like to start or to finish (Section 2.6) to specify the intended reading. It could also be argued that, as with activities, an interjacent meaning is sometimes also possible when punctual adverbials combine with culminating activities. In that case, (2.124) would refer to a flight that was on its way to gate 4 at 5:00 pm. The inchoative or terminal reading, however, is usually much more dominant with culminating activities, and, for simplicity, the interjacent meaning will be ignored. With progressive forms of culminating activity verbs, punctual adverbials normally have only interjacent meanings. Compare, for example, (2.123)– (2.125) to (2.126)–(2.128). This is in accordance with the assumption that the progressive triggers an aspectual shift to state (Section 2.5.3). (2.126) Which flight was landing at 5:00 pm? (2.127) Which flight was taxiing to gate 4 at 5:00 pm? (2.128) Who was inspecting BA737 at 5:00 pm?
Punctual adverbials and past perfect. As already mentioned in Section 2.5.5, in sentences like (2.129) the adverbial can refer either directly to the situation, meaning that the taxiing started or ended at 5:00 pm, or to the reference time, in which case the taxiing had already finished at 5:00 pm. (2.129) BA737 had taxied to gate 2 at 5:00 pm.
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(2.130) BA737 had [taxied to gate 2 at 5:00 pm]. (2.131) BA737 [had taxied to gate 2] at 5:00 pm.
The treatment of sentences like (2.129) in this book will become clearer in Chapter 3. A rough description, however, can be given here. (2.129) is treated as syntactically ambiguous between (2.130), where the adverbial applies to the past participle taxied, and (2.131), where the adverbial applies to the past perfect had taxied. The past participle (taxied) inherits the aspectual class of the base form (culminating activity), and refers directly to the situation of the verb (the taxiing). In contrast, the past perfect (had taxied) is a state, because the past perfect causes an aspectual shift to state (Section 2.5.5). The past perfect refers to a time-period that starts immediately after the end of the situation of the verb (the end of the taxiing) and extends indefinitely. Let us call it the consequent period. In (2.130), then, a punctual adverbial combines with the culminating activity past participle. According to the discussion above, two readings arise: an inchoative reading, whereby the taxiing started at 5:00 pm, and a terminal one, where the taxiing finishes at 5:00 pm. In contrast, in (2.131) the punctual adverbial combines with the past perfect had taxied, which is a state expression that refers to the consequent period. Hence, only an interjacent reading arises: the time of the adverbial must simply be within the consequent period, which implies that the taxiing must have been completed at the time of the adverbial. A similar arrangement is used when the past perfect combines with period adverbials, duration for and in adverbials, or temporal subordinate clauses.
Lexical, consequent, and progressive states. There is sometimes a need to distinguish between expressions that are states because they have inherited the state aspectual class of a base verb form, and expressions that are states because of an aspectual shift introduced by a past perfect or a progressive form. Following Moens (1987), the terms lexical state, consequent state, and progressive state will be used to distinguish the three genres, respectively. In the airport domain, for example, the base form of to contain is a lexical state, while the base form of to queue is an activity. The simple past queued and the past participle queued are also activities. The past perfect had queued is a consequent state, while the present continuous is queueing is a progressive state. Aspectual shift of punctual adverbials. As already briefly mentioned, it is assumed that punctual adverbials cause the aspectual class of the syntactic constituent they modify to become point. This will allow us to account for sen-
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Table 2.2 Punctual adverbials in this book meanings of punctual adverbials with state with activity with culm. activity with point
interjacent inchoative or interjacent inchoative or terminal time of instantaneous situation
The resulting aspectual class is point.
tences with multiple temporal adverbials in Chapter 4. In (2.131), for example, the taxied to gate 2 inherits the culminating activity aspectual class of the base form. The past perfect causes the aspectual class of had taxied to gate 2 to become consequent state. Finally, the at 5:00 pm causes the aspectual class of had departed at 5:00 pm to become point. Table 2.2 summarises the main observations of this section. .. Period adverbials Unlike punctual adverbials, that are understood as specifying points in time, adverbials like in 1999, on Monday, yesterday, as in (2.132)–(2.134), are usually understood as specifying longer, non-instantaneous periods of time. The term period adverbial will be used to refer to them. (2.132) Who was the sales manager in 1999? (2.133) Did BA737 circle on Monday? (2.134) Which flights did J. Adams inspect yesterday?
Before and after adverbials, as in (2.135), can also be considered period adverbials, except that in this case one of the boundaries of the period is left unspecified. In (2.135), for example, the end of the period is the beginning of 2/5/1999; the beginning of the period is left unspecified. Before and after can also introduce temporal subordinate clauses; this will be discussed in Section 2.10.2. (2.135) Which company serviced BA737 before 2/5/1999?
This book examines only period adverbials introduced by in, on, before, and after, as well as today and yesterday. In can also introduce duration adverbials, like in two hours; this will be discussed in Section 2.9.4. Other period adverbials, like from 1996 to 1999, since 1996, last week, or two days ago, will not be considered.
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Period adverbials with states. When period adverbials combine with state expressions, the situation of the state expression must hold for at least some time during the period of the adverbial. In (2.136), for example, the person must have been a manager for at least some time in 1999. Similarly, in (2.137), the person must have been at gate 2 for at least some time on the previous day. (2.136) Who was a manager in 1999? (2.137) Who was at gate 2 yesterday?
There is often, however, an implication that the situation holds throughout the period of the adverbial. (2.138), for example, could mean that the tank was empty throughout January, not at simply some part of January. Similarly, in (2.139) the user could be referring to tanks that were empty throughout January. In that case, if a tank was empty only some days in January and the nlitdb included that tank in the answer, the user would be misled to believe that the tank was empty throughout January. Similar comments can be made for (2.140) and (2.141). (2.138) (2.139) (2.140) (2.141)
Tank 4 was empty in January. Which tanks were empty in January? Was runway 2 open on 6/7/1999? Which flights departed (habitually) from gate 2 in 1999?
The same implication is possible in sentences with before or after adverbials. (2.142), for example, could mean that the runway was open all the time from some unspecified time up to 5:00 pm, and possibly longer. (2.142) Runway 2 was open before 5:00 pm.
One way to deal with such implications is to treat sentences where period adverbials combine with states as ambiguous. That is, to distinguish between a reading where the situation holds throughout the adverbial’s period, and a reading where the situation holds at simply some part of the adverbial’s period. Vlach (1993: 256) uses the terms durative and inclusive to refer to the two readings. An nlitdb could paraphrase both readings and ask the user to select one, or it could provide answers to both readings, indicating which answer corresponds to which reading. This approach has the disadvantage that it always generates two readings, even when the durative reading is clearly impossible. For example, when the state expression combines not only with a period adverbial but also with a for duration adverbial, the meaning can never be that the situation must necessarily hold throughout the period of the period adverbial; (2.143) can never mean that the tank must have been empty throughout Jan-
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uary (cf. (2.139)). Similarly, in time-asking questions like (2.144), the durative reading is impossible. (2.143) Which tank was empty for two days in January? (2.144) When on 6/7/1999 was runway 2 open?
Formulating an account of exactly when the durative reading is possible is difficult. Although Chapter 3 discusses how the distinction between durative and inclusive reading could be captured in top, for simplicity the rest of this book considers only the inclusive reading, ignoring the durative one.
Period adverbials with points. When period adverbials combine with point expressions, as in (2.145), the period of the adverbial must contain the time where the instantaneous situation of the point expression occurs. (2.145) Did BA737 enter sector 5 on Monday?
Period adverbials with culminating activities. Two readings will be allowed when period adverbials combine with culminating activity expressions: (a) that the situation of the culminating activity expression both starts and reaches its completion within the adverbial’s period, and (b) that the situation simply reaches its completion within the adverbial’s period. In the second reading, the culminating activity expression will be treated as referring only to the completion of the situation it would normally denote, and the aspectual class of the overall expression will be shifted to point. The first reading is the preferred one in (2.146), which is most naturally understood as referring to a runner who both started and finished running the forty miles on Wednesday. The verb to run with an object denoting a specific distance is typically classified as culminating activity. (2.146) Who ran 40 miles on Wednesday?
In the airport domain, the first reading is also the preferred one in (2.147), i.e., the inspection both started and was completed on Monday. (2.147) J. Adams inspected BA737 on Monday.
The second reading, that the situation simply reaches its completion within the adverbial’s period, is needed in questions like (2.148) and (2.149). In the airport domain, to land and to take off are culminating activity verbs. If only the first reading were available, in (2.148) the nlitdb would report only flights that both started and finished landing on Monday. If a flight started the landing
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procedure at 23:55 on Sunday and finished it at 00:05 on Monday, that flight would not be reported. This seems over-restrictive; in (2.148), the most natural reading is that the flights must have simply touched down on Monday, and similar comments apply to (2.149) and (2.150) in domains where to fix is a culminating activity verb. (2.148) Which flights landed on Monday? (2.149) Which flights took off after 5:00 pm? (2.150) Did J. Adams fix any faults yesterday?
The problem in these cases is that to land, to take off, and to fix need to be treated as point verbs referring only to the time-points where the corresponding situations were completed, even though they have been classified as culminating activity verbs. The second reading allows exactly this. The culminating activity expression is taken to refer only to the completion point of the situation, its aspectual class is changed to point, and the completion point is required to fall within the adverbial’s period. This arrangement may not always be entirely satisfactory. Let us assume, for example, that J. Adams started inspecting a flight late on Monday, and finished the inspection early on Tuesday. None of the two readings would include that flight in the answer to (2.151), because both require the completion point to fall on Monday. While strictly speaking this seems correct, it would be better if the nlitdb included in the answer inspections that partially overlap the adverbial’s period, warning the user about the fact that these inspections are not completely contained in the adverbial’s period. This is another case where cooperative responses are needed. (2.151) Which flights did J. Adams inspect on Monday?
It should also be noted that with before adverbials, as in (2.152), the two readings are equivalent: requiring the situation to simply reach its completion before some time is equivalent to requiring the situation to both start and reach its completion before that time. To avoid generating equivalent readings, only the reading where the situation both starts and reaches its completion within the adverbial’s period will be admitted in this case. (2.152) Which flights took off before 5:00 pm?
Period adverbials with activities. When period adverbials combine with activities, the situation of the verb must hold for at least some time within the adverbial’s period; this is the same as with states. In (2.153), for example, the
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Table 2.3 Period adverbials in this book meanings of period adverbials with state, activity
The situation holds for at least part of the adverbial’s period.
with culm. activity
The situation starts and is completed within the adverbial’s period, or the situation is simply completed within the adverbial’s period.*†
with point
The situation occurs within the adverbial’s period.
* The second reading is not available with before adverbials. † In the second reading, the resulting aspectual class is point.
In all other cases, the aspectual class remains the same.
flight must have circled for at least some time on Monday, and in (2.154) the flights must have taxied for at least some time after 5:00 pm. (2.153) Did BA737 circle on Monday? (2.154) Which flights taxied after 5:00 pm?
Another stricter reading is sometimes possible, especially with before and after: that the situation does not extend past the boundaries of the adverbial’s period. For example, (2.154) would refer to flights that started to taxi after 5:00 pm; a flight that started to taxi at 4:55 pm and continued to taxi until 5:05 pm would not be reported. This reading may also be possible with states (cf. (2.142)), though with activities it seems easier to accept. As a simplification, readings of this kind will be ignored.
Elliptical forms of period adverbials. Before and after are sometimes followed by noun phrases that do not denote entities of the temporal ontology, as in (2.155). (2.155) Did J. Adams inspect BA737 before UK160? (2.156) Did J. Adams inspect BA737 before he inspected UK160?
Questions like (2.155) can be considered elliptical forms of (2.156), i.e., in these cases before and after could be treated as when they introduce subordinate clauses (see Section 2.10.2 below). Elliptical forms are not examined in this book, and questions like (2.155) will not be discussed further. Table 2.3 summarises the main points of this section. .. Duration adverbials introduced by ‘for’ We now move on to temporal adverbials that specify durations, starting with duration adverbials introduced by for.
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‘For’ adverbials with states and activities. When for adverbials combine with states or activities, one reading is that there must be a period with the duration of the for adverbial, such that the situation of the state or activity holds throughout that period. According to this reading, in (2.157) there must be a five-year period throughout which the person was a manager, and in (2.158) a twenty-minute period throughout which BA737 was circling. If J. Adams was a manager for six consecutive years, for example from 1981 to 1986, he would be reported in (2.157), because there is a five-year period, for example 1981 to 1985, throughout which he was a manager. (2.157) Who was a manager for five years? (2.158) Did BA737 circle for twenty minutes?
In some cases, however, for adverbials are used with a stricter meaning: they specify the duration of a maximal period where a situation held. In that case, if J. Adams started to be a manager at the beginning of 1981 and stopped being a manager at the end of 1986 (six consecutive years), he would not be included in the answer to (2.157). For simplicity, this stricter reading is ignored in this book. In other cases, a for adverbial does not necessarily specify the duration of a single period, but a total duration. According to this reading, if J. Adams was a manager during several non-overlapping periods, and the total duration of these periods is five years, he would be included in the answer to (2.157), even if he was never a manager for a continuous five-year period. This reading of for adverbials is also not considered in this book. It should also be noted that in sentences like (2.159), the duration adverbial can never be understood as specifying the duration of the consequent period (Section 2.9.1). (2.159) BA737 had circled for two hours.
This will be discussed further in Chapter 4 (Section 4.11.3), once some formal apparatus has been established. For the moment, it suffices to say that for adverbials will not be allowed to combine with consequent states.
‘For’ adverbials with points. Adverbials introduced by for sometimes specify the duration of a situation that follows the situation of the verb. This is particularly common with point expressions. For instance, (2.160), which is based on an example by Hwang and Schubert (1994), does not mean that J. Adams was actually leaving his office for fifteen minutes. It means that he stayed, or intended to stay, out of his office for fifteen minutes. It is assumed here that to
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leave is a point verb, as in the airport domain. This use of for adverbials is not considered in this book. (2.160) J. Adams left his office for fifteen minutes.
For adverbials also give rise to iterative readings (Section 2.5.3). This is again particularly common with point expressions, as illustrated by Hwang and Schubert’s example in (2.161); the verb to win is typically classified as point. The sentence has an iterative meaning, whereby Mary won several times. The reader is reminded that iterative readings are not considered in this book. (2.161) Mary won the competition for four years.
Excluding iterative readings and readings where for adverbials refer to consequent situations, sentences in which for adverbials combine with point expressions either sound odd or signal that the user is unaware that the situation of the point expression is modelled as instantaneous. (Ideally, an explanatory message would be produced; yet another case where cooperative responses are needed.) Hence, for the purposes of this book it seems reasonable not to allow for adverbials to combine with point expressions.
‘For’ adverbials with culminating activities. When for adverbials combine with culminating activities, the sentences sometimes sound odd or even unacceptable. For example, to build is typically classified as culminating activity verb. (2.162) sounds odd or unacceptable to most native English speakers. In contrast, (2.163), where the adverbial combines with a progressive state, is easily acceptable. (2.162) ?Housecorp built a shopping centre for two years. (2.163) Housecorp was building a shopping centre for two years.
Based on similar examples, Vendler concludes that ‘accomplishments’ (culminating activities) do not combine with for adverbials (Section 2.2). This, however, seems over-restrictive. For example, (2.164) and (2.165) are acceptable. (2.164) BA737 taxied to gate 2 for two minutes. (2.165) Did J. Adams inspect BA737 for ten minutes?
Unlike (2.166), in (2.164) there is no requirement that the taxiing must have been completed, i.e., that BA737 must have reached the gate. Similar comments can be made for (2.165) and (2.167). For adverbials seem to cancel any requirement that the climax must have been reached. Similar observations are made by Dowty (1986), Moens and Steedman (1988), and Kent (1993).
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Table 2.4 Duration adverbials introduced by ‘for’ in this book meanings of duration adverbials introduced by for with lexical state, progressive state, activity, culminating activity
The situation holds continuously for at least that long.*
with consequent state, point
(Not allowed in the framework of this book.)
* With culminating activities, there is no need for the climax to be reached.
(2.166) BA737 taxied to gate 2. (2.167) Did J. Adams inspect BA737?
The framework of this book allows for adverbials to combine with culminating activities, with the same meaning as in the case of states and activities, but with the proviso that any requirement that the climax must have been reached should be cancelled. That is, in (2.165) there must be a ten-minute period throughout which J. Adams was inspecting BA737; there is no requirement that the inspection must have been completed. Table 2.4 summarises the main points of this section. .. Duration adverbials introduced by ‘in’ This section discusses duration adverbials introduced by in, as in (2.168) and (2.169). Period in adverbials were discussed in Section 2.9.2. (2.168) Airserve serviced BA737 in two hours. (2.169) Which flight did J. Adams inspect in one hour?
‘In’ adverbials with culminating activities. With culminating activity expressions, in adverbials usually specify the length of a period that ends at the timepoint where the situation of the culminating activity is completed. In (2.168), for example, two hours is probably the length of a period that ends at the timepoint where the service was completed. (2.169) is similar. The period whose length is specified by the in adverbial usually starts at the time-point where the situation of the culminating activity begins. In (2.168), for example, the two hours probably start at the time-point where the service began. Sometimes, however, the period of the adverbial may not start at the beginning of the situation of the culminating activity, but at some other earlier time. In (2.168), the start of the two hours could be the time-point where Airserve was asked to service BA737, not the beginning of the actual service. In this book, we will
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consider only the case where the period of the adverbial starts at the beginning of the situation of the culminating activity.
‘In’ adverbials with points. With point expressions, the period of the in adverbial starts before the instantaneous situation of the point expression, and ends at the time-point where the situation of the point expression occurs. In (2.170), the ten minutes end at the point where BA737 arrived at gate 2, and start at some earlier time-point; for example, when BA737 started to taxi to gate 2. (2.171) is similar. (2.170) BA737 reached gate 2 in ten minutes. (2.171) BA737 entered sector 2 in five minutes.
Determining exactly when the period of the adverbial starts, however, is often difficult. It is not clear, for example, when the five minutes of (2.171) start. As a simplification, the framework of this book does not allow duration in adverbials to combine with point expressions.
‘In’ adverbials with states and activities. When in adverbials are used with activity expressions, the speaker sometimes has a culminating activity view in mind. For example, in (2.172) the speaker may have a particular destination, say gate 2, in mind. In that case, (2.172) can be considered an elliptical form of (2.173). Elliptical forms are not examined in this book, and sentences like (2.172) will not be discussed further. (2.172) BA737 taxied in ten minutes. (2.173) BA737 taxied to gate 2 in ten minutes.
With state and activity expressions, in adverbials can also specify the duration of a period that ends at the beginning of the situation of the state or activity expression. In (2.174), for example, the two hours probably end at the timepoint where tank 5 started to be empty. The beginning of the two hours could be, for example, a time-point where a pump started to empty the tank, or a time-point where a decision to empty the tank was taken. A similar reading is available in (2.172). (2.174) Tank 5 was empty in two hours.
As with point expressions, determining exactly when the period of the adverbial starts is often difficult. Again, as a simplification, the framework of this book does not allow duration in adverbials to combine with states and activities. Table 2.5 summarises the main points of this section.
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Table 2.5 Duration adverbials introduced by ‘in’ in this book meanings of duration adverbials introduced by in with state, activity, point
(Not allowed in the framework of this book.)
with culminating activity
Distance from the start to the completion of the situation.
.. Other temporal adverbials The linguistic coverage of this book does not include other kinds of temporal adverbials. Among the temporal adverbials that are not covered are several adverbials that specify boundaries, like until 1/5/1999, since 1997, by Monday, frequency adverbials, like always, twice, every Monday, and adverbials of temporal order, like for the second time and earlier.
. Temporal subordinate clauses Three types of temporal subordinate clauses will be examined in this book: clauses introduced by while, before, and after. .. Clauses introduced by ‘while’ Each while clause can be thought of as contributing a time period. The analysis below examines first how this period is established, and then how it relates to the situation of the main clause.
The period of the ‘while’ clause. The period contributed by the while clause must be a maximal period throughout which the situation of the clause holds. If there are several periods of this kind, then the contributed period can generally be any of them. Let us assume, for example, that J. Adams was a manager only from 1/1/1980 to 31/12/1983 and from 1/1/1987 to 31/12/1990. Then, in (2.175) the period of the while clause can be any of the two periods. In practice, the user may have in mind a particular period period among the two, in which case a temporal anaphora resolution mechanism is needed to determine that period. The framework of this book, however, provides no such mechanism, and the answer to (2.175) will include anybody who was fired during any of the two periods. Temporal anaphora is discussed further in Section 2.12 below. (2.175) Who was fired while J. Adams was a manager?
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Sentences where the aspectual class of the while clause is point, like (2.176) in the airport domain, typically signal that the user is unaware that the situation of the while clause is modelled as instantaneous. In the framework of this book, the answer to (2.176) will include any flight that was circling at the time-point where BA737 entered sector 2. Ideally, a message would also be generated to warn the user that entering a sector is modelled as instantaneous, but no mechanism to generate such cooperative messages is currently in place. (2.176) Which flights were circling while BA737 entered sector 2?
Sentences containing while clauses whose aspectual class is consequent state usually sound unnatural or unacceptable. For example, (2.177)–(2.179) sound at least unnatural, and their intended meanings are unclear. Instead of (2.177), for example, one would normally use (2.180) or (2.181). Hence, while clauses whose aspectual class is consequent state will not be allowed in the framework of this book. (2.177) (2.178) (2.179) (2.180) (2.181)
?Did any flight depart while
BA737 had landed?
?Did ABM fire anybody while Adams had been the manager? ?Had any flight departed while
Adams had inspected BA737? Did any flight depart while BA737 was landing? Did any flight depart after BA737 had landed?
When the aspectual class of the while clause is culminating activity, there is no requirement that the climax of the situation of the while clause must have been reached, even if the verb form of that clause normally requires this. In (2.183) and (2.186), for example, there does not seem to be any requirement that the service or the boarding must have been completed (cf. (2.182) and (2.185)). (2.183) and (2.186) appear to have the same meanings as (2.184) and (2.187). Table 2.6 summarises the main points about while clauses so far. Table 2.6 Periods of ‘while’ clauses in this book while clause
period specified by the while clause
consequent state
(not allowed in the framework of this book)
lexical state, progressive state, activity, culminating activity
maximal period where the situation of the while clause holds*
point
instantaneous period where the situation of the while clause occurs
* When the while clause is culminating activity, there is no need for the climax of its situation to be reached.
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(2.182) (2.183) (2.184) (2.185) (2.186) (2.187)
Did Airserve service BA737? Which flights departed while Airserve serviced BA737? Which flights departed while Airserve was servicing BA737? Did BA737 board? Which flights departed while BA737 boarded? Which flights departed while BA737 was boarding?
Main clause modified by ‘while’ clause. Once the periods of the while clauses have been established following Table 2.6, the behaviour of while clauses appears to be the same as that of period adverbials, i.e., it follows Table 2.3 on page 50. With main clauses whose aspectual class is point, the instantaneous situation of the main clause must occur within the period of the while clause. For example, to depart is a point verb in the airport domain. In (2.188), the departures must have occurred during a maximal period where runway 5 was closed. (2.188) Did any flight depart from gate 2 while runway 5 was closed?
With activity main clauses, the situation of the main clause must be ongoing some time during the period of the while clause. In (2.189), for example, the flights must have taxied some time during a maximal period where BA737 was circling (cf. Table 2.3). Stricter readings are sometimes possible with activity main clauses, as in the case of period adverbials (Section 2.9.2). For example, (2.189) could refer to flights that both started and stopped taxiing during a maximal period where BA737 was circling. As with period adverbials, these stricter readings will be ignored. (2.189) Which flights taxied while BA737 circled?
As in the case of period adverbials, with culminating activity main clauses two readings are allowed: (a) that the situation of the main clause both starts and reaches its completion within the period of the while clause, or (b) that the situation of the main clause simply reaches its completion within the period of the while clause. In the second reading, the main clause is taken to refer only to the completion point of the situation it would normally denote, and its aspectual class is changed to point (cf. Table 2.3). In the airport domain, the first reading is the preferred one in (2.190). The second reading allows the answer to (2.191) to contain flights that simply touched down during the service, even if their landing procedures did not start during the service. (2.190) Adams inspected BA737 while Airserve was servicing UK52. (2.191) Which flights landed while Airserve was servicing UK52?
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With state main clauses, the situation of the main clause is required to hold some time during the period of the while clause; this corresponds to the inclusive reading of Section 2.9.2. For example, the non-auxiliary to be is typically classified as state verb. In (2.192), the answer must contain anybody who was a lecturer some time during a maximal period where Adams was a professor. As with period adverbials, there is often an implication that the situation of the main clause holds throughout the period of the while clause; this corresponds to the durative reading of Section 2.9.2. According to the durative reading, (2.192) refers to people who were lecturers throughout the, presumably unique, maximal period where Adams was a professor; and (2.193), where the main clause is a progressive state, refers to a flight that was circling throughout a maximal period where runway 2 was closed. (2.192) Who was a lecturer while Adams was a professor? (2.193) Which flight was circling while runway 2 was closed?
As with period adverbials, Chapter 3 will demonstrate how durative readings can be captured in top, but these readings will not be considered further in the rest of this book. It should be noted that the treatment of temporal subordinate clauses of this book is in many ways similar to that of Ritchie (1979). Ritchie also views temporal subordinate clauses as establishing periods. The exact relations between these periods and the situations of the main clauses depend on the aspectual classes of the main clauses and the words introducing the subordinate clauses. .. Clauses introduced by ‘before’ and ‘after’ Like the before and after adverbials of Section 2.9.2, clauses introduced by before and after are treated as establishing periods. In before clauses, the period starts at some unspecified time-point; in the absence of other constraints, this is the beginning of time. The end-point of the period is provided by the before clause. In after clauses, the period starts at a time-point provided by the after clause, and ends at some unspecified time-point, or the end of time. The terms beforepoint and after-point will be used to refer to the time-points provided by before and after clauses, respectively. Once the periods of the before and after clauses have been established, the behaviour of the clauses appears to be the same as that of period adverbials, i.e., it follows Table 2.3 on page 50.
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State ‘before’ or ‘after’ clause. Let us first examine sentences where the aspectual class of the before or after clause is state. With before clauses, the beforepoint is a time-point where the situation of the before clause starts (Table 2.7). In (2.194), for example, the before-point is a time-point where runway 2 started to be open. In the airport domain, the aspectual class of the main clause is point. According to Table 2.3 on page 50, the departures must have occurred within the period of the before clause, i.e., before the time-point where runway 2 started to be open. Similar comments apply to (2.195), (2.196), where the before clause is a progressive state, and (2.197), where the before clause is a consequent state. In (2.197), the before-point is the beginning of the consequent period of the inspection (Section 2.9.1), i.e., the beginning of the period that contains all the time after the completion of the inspection. Hence, the departures must have happened before the inspection was completed. (2.194) Which flights departed before runway 2 was open? (2.195) Which flights departed before the emergency system was in operation? (2.196) Which flights departed before BA737 was circling? (2.197) Which flights departed before Adams had inspected BA737?
According to Table 2.3 on page 50, in (2.198) where the main clause is a state, the flight must have been at gate 2 some time during the period of the before clause, i.e., for some time before runway 2 started to be open. In (2.199), where the main clause is an activity, the flight must have circled for some time before runway 2 started to be open. In (2.200), which involves a culminating activity main clause, the inspections must have both started and been completed before runway 2 started to be open. (2.198) Was any flight at gate 2 before runway 2 was open? (2.199) Did any flight circle before runway 2 was open? (2.200) Which flights did J. Adams inspect before runway 2 was open? Table 2.7 Clauses introduced by ‘before’ in this book aspectual class of before clause
before-point (end-point of period specified by before clause)
state, activity
time-point where the situation of the before clause starts
culm. activity
time-point where the situation of the before clause starts or is completed
point
time-point where the situation of the before clause occurs
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As with the before adverbials of Section 2.9.2, in (2.200) it would be better if the nlitdb could also report inspections that started but were not completed before runway 2 opened, warning the user that those inspections were not completed before runway 2 opened. Again, a mechanism for cooperative responses is needed to achieve this. In the case of after clauses, if the aspectual class of the after clause is a lexical or progressive state, the after-point is a time-point where the situation of the after clause either starts or ends (Table 2.8). For example, (2.201) has two readings: that the flights must have departed after runway 2 started to be open, or that the flights must have departed after runway 2 stopped being open. Similar comments apply to (2.202) and (2.203). In practice, additional temporal verbs, like to start or to stop would typically be included to clarify the intended meanings. Knowing the readings that are possible without these verbs, however, is still useful, as it allows the nlitdb to detect the possible ambiguities when users omit them. (2.201) Which flights departed after runway 2 was open? (2.202) Which flights departed after the emergency system was in operation? (2.203) Which flights departed after BA737 was circling?
In sentences like (2.204), where the aspectual class of the after clause is consequent state, the after-point can only be the beginning of the consequent period, i.e., the first time-point after the completion of the inspection. It cannot be the end of the consequent period, because the end of the consequent period is the end of time. This explains the distinction between consequent and lexical or progressive states in Table 2.8. (2.204) Which flights departed after Adams had inspected BA737? Table 2.8 Clauses introduced by ‘after’ in this book aspectual class of before clause
after-point (start-point of period specified by after clause)
lexical or progressive state
time-point where the situation of the after clause starts or ends
consequent state
time-point where the consequent period of the after clause starts
activity
time-point where the situation of the after clause ends
culm. activity
time-point where the situation of the after clause is completed
point
time-point where the situation of the before clause occurs
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Point ‘before’ or ‘after’ clause. If the aspectual class of the before or after clause is point, the before- or after-point is the time-point where the instantaneous situation of the subordinate clause occurs. In (2.205), for example, the beforeor after-point is the point where BA737 reached gate 2. (2.205) Which flights departed before/after BA737 reached gate 2?
Activity ‘before’ or ‘after’ clause. With activity before clauses, the before-point is a time-point where the situation of the before clause starts. In (2.206) and (2.207), for example, the departures must have occurred before BA737 started to taxi or circle. (2.206) Which flights departed before BA737 taxied? (2.207) Which flights departed before BA737 circled?
With activity after clauses, the after-point must be a point where the situation of the after clause ends. In (2.208) and (2.209), for example, the departures must have occurred after BA737 stopped taxiing or circling. (2.208) Which flights departed after BA737 taxied? (2.209) Which flights departed after BA737 circled?
Another reading may sometimes be possible with after clauses: that the afterpoint is a time-point where the situation of the after clause starts. In this case, (2.209) would refer to departures that occurred after BA737 started to circle. This reading, however, seems less likely, and for simplicity it will be ignored. Again, in practice people would probably use additional temporal verbs, like to start or to stop, to clarify the intended meaning.
Culminating activity ‘before’ or ‘after’ clause. With after clauses whose aspectual class is culminating activity, the after-point is most likely a time-point where the situation of the after clause reaches its completion. In (2.210), for example, the most probably reading is that the departures must have occurred after the completion of the inspection, and in (2.211) after the time-point where BA737 reached gate 2. These questions may sound slightly unnatural, probably because in practice additional temporal verbs would be used to clarify their meanings. As commented above, however, there is value in attempting to identify the most likely readings in the absence of such verbs. (2.210) Which flights departed after J. Adams inspected BA737? (2.211) Which flights departed after BA737 taxied to gate 2?
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With culminating activity before clauses, the before-point will be allowed to be a time-point where the situation of the before clause either starts or reaches its completion. In the airport domain, the first reading seems the preferred one in (2.212). The flights must have departed before the beginning of the inspection. The second reading seems the preferred one in (2.213). The flights must have departed before the completion of the landing. Both readings seems possible in (2.214). (2.212) Which flights departed before J. Adams inspected BA737? (2.213) Which flights departed before BA737 landed? (2.214) Which flights departed before BA737 taxied to gate 2?
The simple past of culminating activity verbs normally requires the climax to have been reached. However, if the first reading above is adopted, i.e., if the situation of the before clause starts at the before-point, and the clause is in the simple past, it is unclear if the situation of that clause must have necessarily reached its climax. For example, let us assume that the first reading is adopted in (2.212). Should the before-point be the beginning of an inspection that was necessarily completed, or can it also be the beginning of an inspection that was never completed? The framework of this book currently adopts the first approach, but this is probably over-restrictive. It would be better if the nlitdb allowed the before-point to be the beginning of both inspections that were and were not completed, warning the user about inspections that were not completed. This is another case for cooperative responses.
Other uses. Before and after can be preceded by expressions specifying durations, as in (2.215). This use of before and after is not considered in this book. (2.215) BA737 reached gate 2 five minutes after UK160 departed.
Before clauses also have counter-factual uses. For example, in (2.216), which is borrowed from an earlier form of Crouch and Pulman (1993), the situation where the car runs into the tree never takes place. This use of before is not considered in this book. (2.216) Smith stopped the car before it ran into the tree.
.. Other temporal subordinate clauses Temporal subordinate clauses that are not examined in this book include, for example, clauses introduced by since, until, and when. From these, when clauses
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seem the most challenging, as they often require large amounts of common sense knowledge to interpret (Ritchie 1979; Yip 1985; Hinrichs 1986; Moens 1987; Moens & Steedman 1988; Lascarides & Oberlander 1993). .. Tense coordination Some combinations of tenses in the main and subordinate clauses are unacceptable, as demonstrated in (2.217) and (2.218). This book makes no attempt to account for the unacceptability of such combinations. The reader is referred to Harper and Charniak (1986), and Brent (1990) for methods that could be used to reject sentences of this kind. (2.217) *BA737 left gate 2 before runway 2 is free. (2.218) *Which runways are closed while runway 2 was circling?
. Noun phrases and temporal reference A question like (2.219) can refer either to the present sales manager or to the person who was the sales manager in 1999. Similarly, (2.220) may refer either to present students or last year’s students. In (2.221), which closed runway probably refers to a runway that is currently closed, while in (2.222) a closed runway probably refers to a runway that was closed at the time of the landing. (2.219) (2.220) (2.221) (2.222)
What was the salary of the sales manager in 1999? Which students failed in physics last year? Which closed runway was open yesterday? Did BA737 ever land on a closed runway in 1999?
It seems that noun phrases like the sales manager, which students, a closed runway refer either to the present or to the time of the verb tense, if this time is different than the present. In (2.219), the simple past refers to some time in 1999. Therefore, there are two options: the sales manager can refer either to the present sales manager or to somebody who was the sales manager in 1999. Similar comments apply to (2.220). In contrast, in (2.223) the verb tense refers to the present. Hence, there is only one possibility: the sales manager refers to the present sales manager. (2.223) What is the salary of the sales manager?
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In (2.221), the verb tense refers to a time within the previous day where the runway was open. There should be two readings: it should be possible for which closed runway to refer either to a currently closed runway, or to a runway that was closed at the time it was open. Since a runway cannot be closed and open at the same time, the second reading is ruled out. This clash, however, cannot be spotted easily by an nlitdb without some inferential capability. Unfortunately, the hypothesis that noun phrases refer either to the present or the time of the verb tense is not always adequate. For example, a person submitting (2.224) to the nlitdb of a university most probably refers to previous students of the university. In contrast, the hypothesis predicts that the question can refer only to current students. Enc (1986) provides similar examples. (2.224) How many of our students are now professors?
The hypothesis also predicts that (2.225) can refer only to current Prime Ministers or to persons that were Prime Ministers at the time they were born, an extremely unlikely reading. There is, however, a reading where the question refers to all past and present Prime Ministers. This reading is incorrectly ruled out by the hypothesis. (2.225) Which Prime Ministers were born in Scotland?
Hinrichs (1988) argues that determining the times to which noun phrases refer is part of a more general problem of determining the entities to which noun phrases refer. According to Hinrichs, a noun phrase like every admiral generally refers to anybody who was, is, or will be an admiral of any fleet in the world at any time. If, however, (2.226) is uttered in a context where the current personnel of the U.S. fleet is being discussed, the temporal scope of every admiral is restricted to current admirals, in the same way that the scope of every admiral is restricted to admirals of the U.S. fleet. (2.226) Every admiral graduated from Annapolis.
The fact that Hinrichs does not limit the times of the noun phrases to the present and the time of the verb tense is in accordance with the fact that our students in (2.224) is not limited to present students, and the fact that which Prime Ministers in (2.225) may refer to all past and present Prime Ministers. Hinrichs’ approach, however, requires some mechanism to restrict the scope of noun phrases as the discourse evolves, and Hinrichs offers only a very limited sketch of how such a mechanism could be constructed. Also, in the absence of previous discourse, Hinrichs’ treatment suggests that (2.219) refers to the sales managers of all times, an unlikely interpretation. The hypothesis that
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noun phrases refer either to the present or to the time of the verb tense performs better in this case. Given these problems with Hinrichs’ approach, this book adopts the initial hypothesis that noun phrases refer to the present or the time of the verb tense. An alternative approach would be to attempt to merge this hypothesis with Hinrichs’ method; Dalrymple (1988) goes towards that direction. A further improvement, however, can be made to the initial hypothesis. When a noun phrase is the complement of the predicative to be, it seems that the noun phrase can refer only to the time of the verb tense. For example, (2.227) can only be a request to report the 1999 sales manager, not the current sales manager. Similarly, (2.228) cannot mean that J. Adams is the current sales manager. This also accounts for the fact that in (2.219) the salary of the sales manager, i.e., the complement of was, can refer only to a 1999 salary, not to a present salary, unlike the sales manager which can refer either to the present or 1999. The restriction that the complement of the predicative to be must refer to the time of the verb tense does not extend to noun phrases that are subconstituents of that complement, like the sales manager in (2.219). (2.227) Who was the sales manager in 1999? (2.228) J. Adams was the sales manager in 1999.
The same restriction applies to bare adjectives used as complements of the predicative to be. In (2.221), open can only refer to runways that were open on the previous day. It cannot refer to currently open runways. The hypothesis that noun phrases refer to the present or the time of the verb tense does not apply when a temporal adjective, like current, specifies explicitly the time of the noun phrase, as in (2.229). (2.229) Which current students failed in Physics last year?
In Chapter 4, an additional mechanism will be introduced, which allows the person configuring the nlitdb to force some noun phrases to be treated as referring always to the time of the verb tense, or always to the present.
. Temporal anaphora There are several English expressions, like that time, the following day, then, later that refer implicitly to contextually salient times, in a way that is similar to how pronouns, possessive determiners, etc. refer to contextually salient world entities. The terms temporal and nominal anaphora are used to refer to these
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two phenomena; Partee (1984) discusses the parallels between temporal and nominal anaphora further. For example, the user of an nlitdb may submit (2.230), followed by (2.231). In (2.231), at that time refers to the time when John became manager, an instance of temporal anaphora. In a similar manner, he refers to John, a case of nominal anaphora. (2.230) When did John become manager? (2.231) Was he married at that time?
Names of months, days, etc. often have a similar temporal anaphoric nature. For example, in a context where several questions about the 1996 status of a company have just been asked, (2.232) most probably refers to the January of 1996, not any other January. In the absence of previous questions, (2.232) most probably refers to the January of the current year. Kamp and Reyle (1993: 613– 634) provide related discussion. (2.232) Who was the sales manager in January?
Verb tenses also seem to have a temporal anaphoric nature. The term tense anaphora is often used in this case. For example, the user may ask (2.233). Let us assume that the response is negative, and that the user then asks (2.234). In that case, the simple past was of (2.234) does not refer to an arbitrary past time. It refers to the past time of the previous question, i.e., 1998. (2.233) Was Mary the personnel manager in 1998? (2.234) Who was the personnel manager?
The anaphoric nature of verb tenses is clearer in multi-sentence text (Hinrichs 1986; Webber 1988; Kamp & Reyle 1993; Kameyama, Passonneau, & Poesio 1993). In (2.235), for example, the simple past landed refers to a landing that happened immediately after the permission of the first sentence was given. It does not refer to an arbitrary past time where BA737 landed on runway 2. Similar comments apply to taxied. Text of this form will not be considered in this book. (2.235) BA737 was given permission to land at 5:00 pm. It landed on runway 2, and taxied to gate 4.
In dialogues like those of (2.233) and (2.234), a simplistic treatment of tense anaphora is to store the time of the adverbial of (2.233), and require the simple past of (2.234) to refer to that time. A more elaborate version of this approach will be sketched in Chapter 3, but it will not be considered any further. The behaviour of noun phrases like the sales manager of Section 2.11 can also be seen
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as a case of temporal anaphora. This is the only type of temporal anaphora that will be supported by the theoretical framework of this book. Expressions like at that time, the following day, etc. will not be examined, and verb forms referring to the past will be taken to refer to any past time. For example, (2.234) will be taken to refer to anybody who was the personnel manager at any past time.
. Phenomena that will not be considered We will now touch upon some additional time-related linguistic phenomena that will not be examined further in this book.
Cardinality and duration questions. Questions about the cardinality of a set or the duration of a situation, as in (2.236) and (2.237), will not be examined. This simplifies the definition of top in Chapter 3. (2.236) How many flights have landed today? (2.237) For how long was tank 2 empty?
Cardinality expressions and plurals. Although duration expressions like five hours will be considered, expressions specifying cardinalities of sets, like eight passengers or two airplanes, will be ignored. Expressions of the latter type give rise to a distinction between distributive and collective readings (Stirling 1985; Crouch & Pulman 1993). For example, (2.238) has a collective reading where the eight passengers arrive at the same time, and a distributive one where there are eight separate arrivals. To simplify top, cardinality expressions of this kind will not be examined. (2.238) Eight passengers arrived.
Furthermore, plural noun phrases introduced by some and which, like some flights and which passengers, will be treated semantically as singular. For example, (2.239) and (2.241) will be treated as having the same meanings as (2.240) and (2.242), respectively. (2.239) (2.240) (2.241) (2.242)
Which flights landed? Which flight landed? Some flights entered sector 2. A flight entered sector 2.
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Quantifiers. Expressions introducing universal quantifiers, like every and all, will not be considered. This leaves only existential quantifiers at the logical level, and an interrogative version of them, which will be discussed in Chapter 3, avoiding issues related to quantifier scoping. More information about the task of quantifier scoping will be provided in Chapter 6. Conjunction, disjunction, and negation. Conjunctions of words or phrases will not be considered. Among other things, this avoids phenomena related to sequencing of events (Hinrichs 1986; Hinrichs 1988; Webber 1988; Kamp & Reyle 1993; ter Meulen 1994; Hwang & Schubert 1994). For example, (2.243) is understood as saying that the patient died after, and probably as a result of, being given Qdrug (cf. (2.244)). In contrast, in (2.245) the patient was given Qdrug while he had high fever. (2.243) Which patient was given Qdrug and died? (2.244) ?Which patient died and was given Qdrug? (2.245) Which patient had high fever and was given Qdrug?
Expressions introducing disjunction or negation, like or, either, not, never, will also not be considered. This simplifies top and the mapping to database language. Not supporting negation also avoids various temporal phenomena related to negation (Kamp & Reyle 1993: 546–555), and observations that negation causes aspectual shifts (Dowty 1986; Moens 1987).
Relative clauses. Relative clauses require special temporal treatment. For example, (2.246) most probably does not refer to a runway that was closed at an arbitrary past time. It probably refers to a runway that was closed at the time of the landing. The relation between the time of the relative clause and that of the main clause can vary. Dowty (1986) provides the example of (2.247), where the woman may have seen John during, before, or even after the stealing. (2.246) Which flight landed on a runway that was closed? (2.247) The woman that stole the book saw John.
Relative clauses can also be used with nouns that refer to the temporal ontology, like period in (2.248). (2.248) Who was fired during the period that J. Adams was personnel manager?
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Kamp and Reyle (1993: 663–664) provide additonal examples of temporal phenomena that involve relative clauses. As a simplification, relative clauses will not be considered in this book.
Passives. To simplify the hpsg grammar of Chapter 4, this book concentrates on active voice verb forms. It should be easy to extend the mechanisms of this book to cover passive forms as well.
. Summary This book uses an aspectual taxonomy of four classes: states, points, activities, and culminating activities. The taxonomy classifies verb forms, verb phrases, clauses, and sentences. Whenever the nlitdb is configured for a new application, the base form of each verb is assigned to one of the four aspectual classes. All the other verb forms normally inherit the aspectual class of the base form. Verb phrases, clauses, and sentences normally inherit the aspectual classes of their main verb forms. However, some linguistic mechanisms, like the progressive or some temporal adverbials, may cause the aspectual class of a verb form to differ from that of its base form, or the aspectual class of a verb phrase, clause, or sentence to differ from that of its main verb form. The aspectual taxonomy plays an important role in most time-related linguistic phenomena. Six verb forms are examined in this book: simple present, simple past, present continuous, past continuous, present perfect, and past perfect; various simplifications have been introduced in their meanings. Some special temporal verbs were also identified; from these, to start, to begin, to stop, and to finish will be considered. Among temporal nouns, this book considers nouns like year, month, day, etc., and proper names like Monday, January, and 1/5/1999. Temporal adjectives, are not considered, with the exception of current, which will be used to demonstrate the anaphoric behaviour of some noun phrases. Among temporal adverbials, this book focuses on punctual adverbials, like at 5:00 pm, period adverbials introduced by on, in, before, or after, today and yesterday, and duration adverbials introduced by for and in. Temporal subordinate clauses are similar to temporal adverbials; this book considers subordinate clauses introduced by while, before, and after. Temporal anaphora is not considered in any detail, with the exception of the temporal anaphoric nature of noun phrases. Table 2.9 summarises in more detail the time-related linguistic phenomena of this book.
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Chapter 2
Table 2.9 Coverage of time-related linguistic phenomena in this book verb forms
temporal verbs temporal nouns
temporal adjectives temporal adverbials
subordinate clauses
anaphora
other phenomena
√ simple present (excluding scheduled meaning) √ simple past √ present continuous (excluding future meaning) √ past continuous (excluding future meaning) √ present perfect (treated as simple past) √ past perfect × other forms √ to start, to begin, to stop, to finish × other temporal verbs (e.g., to happen, to follow) √ year, month, day, etc. × period, event, time, etc. × nouns introducing situations (e.g., inspection) × nouns of temporal order (e.g., predecessor) × (only current) √ punctual adverbials (e.g., at 5:00 pm) √ period adverbials (only those introduced by on, in, before, or after, and today, yesterday) √ for duration adverbials √ in duration adverbials (only with culm. act. verbs) × frequency adverbials (e.g., twice) × order adverbials (e.g., for the second time) × other boundary adverbials (e.g., since 1997) √ while clauses √ before and after clauses × relative clauses × other subordinate clauses (e.g., introduced by when) √ noun phrases and temporal reference × January, August, etc. (taken to refer to any of them) × tense anaphora × that time, the following day, etc. × iterative meanings × cardinality and duration queries (how many/long) × cardinality expressions (e.g., five flights) and plurals × conjunctions of words or phrases × expressions introducing universal quantifiers, disjunction, negation
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Chapter 3
The TOP meaning representation language
“Time will tell.”
. Introduction This chapter defines top, the intermediate meaning representation language that will be used to represent the semantics of the English questions before translating them into database language. As already mentioned in Chapter 1, top employs temporal operators. For example, (3.1) is represented in top as (3.2). Roughly speaking, the Past operator requires contain(tank2, water) to be true at some past time ev , and the At operator requires that time to fall within 1/10/1999. The answer to (3.1) is affirmative iff (3.2) evaluates to true. (3.1) Did tank 2 contain water (some time) on 1/10/1999? (3.2) At[1/10/1999, Past[ev , contain(tank2, water)]]
An alternative operator-less approach is to introduce time as an extra argument of each predicate (Section 1.4). Temporal operators, however, lead to more compact formulae, and make the semantic contribution of each linguistic mechanism easier to see. In (3.2), for example, the simple past contributes the Past operator, while the on adverbial contributes the At operator. It is, nevertheless, entirely possible to capture the semantics of temporal linguistic mechanisms using operator-less representations, or to devise additional mappings to translate from top to operator-less representations (Androutsopoulos 2000); the latter will be discussed further in Chapter 7. top is period-based, in the sense that the truth of a top formula is evaluated with respect to a time-period, i.e., a segment of the time-axis, rather than an individual time-point. A top formula may be true at a time-period without being true at the subperiods of that period. More precisely, following the Reichenbachian tradition (Reichenbach 1947), top formulae are evaluated with respect to three times: speech time (st), which is the time when the question is submitted, event time (et), which is a time when the situation described by
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the formula holds, and localisation time (lt), a temporal window within which et must be placed. top’s localisation time is different from Reichenbach’s ‘reference time’ (Section 2.5.5), but similar to the ‘location time’ of Kamp and Reyle (1993). While st is always a time-point, et and lt are generally periods, which is why top can be considered period-based, and in that sense similar to formal languages employed by Dowty (1982), Allen (1984), Lascarides (1988), Richards et al. (1989), Pratt and Bree (1995), and others. top was influenced by the representation language of Crouch and Pulman (1993), which was used in a natural language interface to a planner; see also Pirie et al. (1990). Comparisons between the two languages will be made at several points in this chapter, to demonstrate alternatives. Although the aspectual classes of linguistic expressions affect how these expressions are represented in top, it is not always possible to tell the aspectual class of a linguistic expression by examining the corresponding top formula. The approach here is different from those of Dowty (1977; 1986), Lacarides (1988), and Kent (1993), where aspectual class is a property of formulae or denotations of formulae.
. The syntax of TOP Let us first define top’s syntax. Informal comments about the semantics of top will also be given, to make the syntax definition easier to follow. The semantics of top, however, will be defined formally in later sections.
Terms. Two disjoint sets of strings, CONS and VARS, are assumed. CONS contains all the top constants, and VARS all the top variables. The suffix ‘v ’ distinguishes variables from constants. For example, runwayv, gatev ∈ VARS, while ba737, 1/5/1999 ∈ CONS. TERMS is the set CONS ∪ VARS; it contains top’s terms. Predicate functors. PFUNS is a set containing all the strings that can be used as predicate functors in top’s atomic formulae; this will be discussed further below. Complete partitioning names. CPARTS is a set containing all the strings that can be used as names of complete partitionings of the time-axis. A complete partitioning of the time-axis is a set of consecutive non-overlapping periods, such that the union of all the periods covers the whole time-axis. A formal def-
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The TOP meaning representation language
inition will be given in later sections. For example, the word day corresponds to the complete partitioning that contains the period which covers exactly the day 13/10/1999, the period which covers exactly 14/10/1999, etc. No two dayperiods overlap, and together all the day-periods cover the whole time-axis. Similarly, month corresponds to the partitioning that contains the period for October 1999, the period for November 1999, etc. The suffix ‘c ’ is used with elements of CPARTS; for example, dayc , monthc .
Gappy partitioning names. GPARTS is a set containing all the strings that can be used as names of gappy partitionings of the time-axis. A gappy partitioning of the time-axis is a set of non-overlapping periods, such that the union of all the periods does not cover the whole time-axis. For example, the word Monday corresponds to the gappy partitioning that contains the period which covers exactly the Monday 19/3/2001, the period which covers exactly the Monday 26/3/2001, etc. No Monday-period overlaps another Monday-period, and all the Monday-periods together do not cover the whole time-axis. Similarly, the English expression 5:00 pm can be taken to denote the gappy partitioning that contains the period which covers exactly the 5:00 pm minute of 24/10/1999, the period which covers the 5:00 pm minute of 25/10/1999, etc. The suffix ‘g ’ is used with elements of GPARTS; for example, mondayg , 5:00pmg . Partitioning names. PARTS is the set CPARTS ∪ GPARTS. Atomic formulae. AFORMS contains all the atomic formulae of top. It is the smallest possible set, such that: –
–
If π ∈ PFUNS, and τ1 , τ2 , . . . , τn ∈ TERMS, then π(τ1 , τ2 , . . . , τn ) ∈ AFORMS. π(τ1 , τ2 , . . . , τn ) is called a predicate. τ1 , τ2 , . . . , τn are the arguments of the predicate. If σ ∈ PARTS, β ∈ VARS, and νord ∈ {. . . , –3, –2, –1, 0}, then Part[σ, β, νord ] ∈ AFORMS and Part[σ, β] ∈ AFORMS.
Greek letters are used as meta-variables, i.e., they stand for expressions of top. Predicates, like be at(ba737, gatev ), describe situations in the world. Part[σ, β, νord ] means that β is a period in the partitioning σ. The νord is used to select a particular period from the partitioning. If νord = 0, then β is the current period of the partitioning, i.e., the period that contains st. If νord < 0, then β is the –νord -th period of the partitioning before the current one. When there is no need to select a particular period from a partitioning, the Part[σ, β] form is used.
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Yes/no formulae. Yes/no formulae represent questions that are to be answered with a yes or no (e.g., ‘Is BA737 circling?’). YNFORMS is the set of all these formulae. It is the smallest possible set, such that if π ∈ PFUNS, τ, τ1 , . . . , τn ∈ TERMS, φ, φ1 , φ2 ∈ YNFORMS, σc ∈ CPARTS, νqty ∈ {1, 2, 3, . . . }, and β ∈ VARS, then all the following hold: – – – – – – – – –
AFORMS ⊆ YNFORMS φ1 ∧ φ2 ∈ YNFORMS Pres[φ], Past[β, φ], Perf [β, φ] ∈ YNFORMS At[τ, φ], At[φ1 , φ2 ] ∈ YNFORMS Before[τ, φ], Before[φ1 , φ2 ], After[τ, φ], After[φ1 , φ2 ] ∈ YNFORMS Ntense[β, φ], Ntense[now*, φ] ∈ YNFORMS For[σc , νqty , φ], Fills[φ] ∈ YNFORMS Begin[φ], End[φ] ∈ YNFORMS Culm[π(τ1 , . . . , τn )] ∈ YNFORMS
In the expressions above, β must not occur in φ. This restriction simplifies the translation to database language of Chapter 5, without imposing any additional restrictions to the linguistic coverage. No negation and disjunction connectives are defined, because English expressions introducing these connectives are not considered (Section 2.13). For the same reason, no universal quantifiers are defined. All variables can be thought of as existentially quantified; hence, no explicit existential quantifier is needed. An informal explanation of the operators above follows; their semantics will be defined formally, using st, et, and lt in subsequent sections. Pres[φ] means that φ is true at the present. For example, (3.3) is represented as (3.4). Past[β, φ] means that φ is true at some past time β. The Perf operator is used along with the Past operator to express the past perfect. For example, (3.5) and (3.7) are represented as (3.6) and (3.8), respectively. Roughly speaking, ev and e2v act as pointers to the times where the runway was open, while e1v points to the reference time of the past perfect (Section 2.5.5); the role of these variables will become clearer in later sections. (3.3) (3.4) (3.5) (3.6) (3.7) (3.8)
Runway 2 is open. Pres[open(runway2)] Runway 2 was open. Past[ev , open(runway2)] Runway 2 had been open. Past[e1v , Perf [e2v , open(runway2)]]
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At[τ, φ] means that φ holds some time within a period τ, and At[φ1 , φ2 ] means that φ2 holds at some time where φ1 holds. For example, (3.9) and (3.11) are represented as (3.10) and (3.12), respectively. (3.9) (3.10) (3.11) (3.12)
Runway 2 was open (some time) on 1/1/1999. At[1/1/1999, Past[ev , open(runway2)]] Runway 2 was open (some time) while BA737 was circling. At[Past[e1v , circling(ba737)], Past[e2v , open(runway2)]]
Before[τ, φ] means that φ is true at some time before a period τ, and Before[φ1 , φ2 ] means that φ2 is true at some time before a time where φ1 is true. After[τ, φ] and After[φ1 , φ2 ] have similar meanings. For example, (3.13) and (3.15) are represented as (3.14) and (3.16), respectively. (3.13) (3.14) (3.15) (3.16)
Tank 2 was empty (some time) after 1/1/1999. After[1/1/1999, Past[ev , empty(tank2)]] Tank 2 was empty (some time) before the bomb exploded. Before[Past[e1v , explode(bomb)], Past[e2v , empty(tank2)]]
Ntense is used to capture the anaphoric nature of noun phrases (Section 2.11). Ntense[β, φ] means that φ holds at a time β, and Ntense[now*, φ] means that φ holds at the present. The reading of (3.17) that refers to the person who was the president during the visit is represented as (3.18); the reading that refers to the current president is represented as (3.19). (3.17) The president was visiting Edinburgh. (3.18) Ntense[e1v , president(pv )] ∧ Past[e1v , visiting(pv , edinburgh)] (3.19) Ntense[now*, president(pv )] ∧ Past[e1v , visiting(pv , edinburgh)]
For[σc , νqty , φ] means that φ holds throughout a period that is νqty σc -periods long. For example, (3.20) is represented as (3.21). (3.20) Runway 2 was open for two days. (3.21) For[dayc , 2, Past[ev , open(runway2)]]
The Fills operator can be used to capture durative readings (Section 2.9.2). The reading of (3.22) whereby the tank was empty throughout 1998 is captured by (3.23). In contrast, (3.24) means that the tank was empty some time in 1998, but not necessarily throughout that year. (3.22) Tank 2 was empty in 1998. (3.23) At[1998, Past[ev , Fills[empty(tank2)]]] (3.24) At[1998, Past[ev , empty(tank2)]]
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Begin[φ] refers to a time-point where the situation denoted by φ starts, and End[φ] to a point where it stops. For example, (3.25) and (3.27) can be represented as (3.26) and (3.28), respectively. (3.25) (3.26) (3.27) (3.28)
BA737 started to land. Past[ev , Begin[landing(ba737)]] Tank 2 stopped being empty. Past[ev , End[empty(tank2)]]
Finally, Culm is used to represent sentences where culminating activity verbs appear in forms that require the climax to have been reached. The Culm operator will be discussed further in subsequent sections.
Wh-formulae. Wh-formulae are used to represent questions that contain interrogatives (e.g., ‘Which/Who/When . . . ?’). WHFORMS is the set of all whdef
formulae. WHFORMS = WHFORMS1 ∪ WHFORMS2 , where: –
–
WHFORMS1 is the set of the expressions ?β1 ?β2 . . . ?βn φ, where β1 , β2 , . . . , βn ∈ VARS, φ ∈ YNFORMS, and each one of β1 , β2 , . . . , βn occurs at least once within φ. WHFORMS2 is the set of all the expressions ?mxl β1 ?β2 ?β3 . . . ?βn φ, where β1 , β2 , β3 , . . . , βn ∈ VARS, φ ∈ YNFORMS, each one of β2 , . . . , βn occurs at least once within φ, and β1 occurs at least once within φ as the first argument of a Past, Perf , At, Before, After, or Ntense operator, or as the second argument of a Part operator.
The ‘?’ is the interrogative quantifier, and ‘?mxl ’ is the interrogative-maximal quantifier. The interrogative quantifier is similar to an explicit existential quantifier, but it has the additional effect of reporting the values of its variables that satisfy its scope. Intuitively, ?β1 ?β2 . . . ?βn φ means “report all β1 , β2 , . . . , βn , such that φ”. For example, (3.29) is represented as (3.30). (3.29) Which runways are open? (3.30) ?rv Ntense[now*, runway(rv )] ∧ Pres[open(rv )]
The constraint that each one of β1 , . . . , βn must occur at least once within φ rules out meaningless formulae like ?ov Past[manager(john)], where the ov does not have any relation to the rest of the formula. This constraint is similar to the notion of safety in datalog (Ullman 1988), and is needed in the translation from top to database language; see also van Gelder and Topor (1991).
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The interrogative-maximal quantifier is similar, except that it reports only maximal periods. ?mxl is intended to be used only with variables that denote periods, and this is why in the case of ?mxl the syntax of top requires β1 to occur at certain positions that guarantee it will denote a period. Intuitively, ?mxl β1 ?β2 . . . ?βn φ means “report all the maximal periods β1 , and all β2 , . . . , βn , such that φ”. The interrogative-maximal quantifier is used in ‘When . . . ?’ questions, where we want the answer to contain only the maximal periods during which a situation held, not all of these periods. If, for example, gate 2 was open from 9:00 am to 11:00 am and from 3:00 pm to 5:00 pm, we want the answer to (3.31) to contain only the two maximal periods 9:00 am to 11:00 am and 3:00 pm to 5:00 pm, not any of their subperiods, like 9:30 am to 10:30 am. To achieve this, the question is represented as (3.32). (3.31) When was gate 2 open? (3.32) ?mxl ev Past[ev , open(gate2)]
Formulae. FORMS, the set of all top formulae, is the union YNFORMS ∪ WHFORMS.
. TOP’s temporal ontology Before proceeding to the semantics of top, we will examine more closely the temporal ontology on which top is based. top assumes that time is discrete, linear, bounded, and consisting of timepoints. PTS is the set of all time-points. More formally, a binary precedence relation ≺ over PTS × PTS is assumed, and time is taken to have the following properties: – – – –
–
If t1 , t2 , t3 ∈ PTS, t1 ≺ t2 , and t2 ≺ t3 , then t1 ≺ t3 (transitivity). If t ∈ PTS, then t ≺ t does not hold (irreflexivity). If t1 , t2 ∈ PTS and t1 = t2 , then exactly one of the following holds: t1 ≺ t2 or t2 ≺ t1 (linearity). There is a tfirst ∈ PTS, such that for all t ∈ PTS, tfirst t (left boundedness). Similarly, there is a tlast ∈ PTS, such that for all t ∈ PTS, t tlast (right boundedness). For every t1 , t2 ∈ PTS, with t1 = t2 , there is at most a finite number of t3 ∈ PTS, such that t1 ≺ t3 ≺ t2 (discreteness).
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Hereafter, next(t1 ) denotes the time-point immediately after t1 . More formally, if t1 ∈ PTS – {tlast }, then next(t1 ) = t2 iff t2 ∈ PTS, t1 ≺ t2 , and for no t3 ∈ PTS is it true that t1 ≺ t3 ≺ t2 . In a similar manner, if t1 ∈ PTS – {tfirst }, then prev(t1 ) denotes the time-point immediately before t1 . Below, whenever next(t) is used, it is assumed that t = tlast . Similarly, when prev(t) is used, t = tfirst . A period p is a non-empty subset of PTS with the following property: –
If t1 , t2 ∈ p, t3 ∈ PTS, and t1 ≺ t3 ≺ t2 , then t3 ∈ p (convexity).
PERIODS is the set of all periods. PERIODS* is the set PERIODS ∪ {∅}, i.e., PERIODS* contains also the empty set, which is not a period. A period that contains only one time-point is called an instantaneous period. INSTANTS is the set of all instantaneous periods. Note that the term ‘interval’ is often used in the literature instead of ‘period’. Unfortunately, the database language of Chapter 5 assigns a different meaning to ‘interval’. Hence, this book uses ‘period’ instead of ‘interval’. Iff p1 , p2 ∈ PERIODS and p1 ⊆ p2 , then p1 is a subperiod of p2 . The notation p1 p2 is used in this case; p1 ⊆ p2 is weaker than p1 p2 , because it does not guarantee that p1 , p2 ∈ PERIODS. Iff p1 , p2 ∈ PERIODS and p1 ⊂ p2 , then p1 is a proper subperiod of p2 , written p1 p2 . The definitions of superperiod and proper superperiod are similar. If S is a set of periods, then mxlpers(S) is the set of maximal periods of S. A period of S is maximal iff it is not a proper subperiod of another period in S. If S ⊆ PTS, minpt(S) and maxpt(S) denote the earliest and latest timepoints in S, respectively. Following standard conventions, [t1 , t2 ] denotes the set {t ∈ PTS | t1 t t2 }, and (t1 , t2 ] denotes the set {t ∈ PTS | t1 ≺ t t2 }. [t1 , t2 ) and (t1 , t2 ) are defined similarly.
. TOP model We now turn to the semantics of top, defining first top’s models. A top model is a tuple M = OBJS, fcons , fpfuns , fculms , fgparts , fcparts , such that PERIODS ⊆ OBJS, and fcons , fpfuns , fculms , fgparts , and fcparts are as below. OBJS is a set containing all the objects in the modelled world that can be denoted by top terms. In the airport domain, for example, OBJS contains all the gates and runways of the airport, the inspectors, the flights, etc. The constraint PERIODS ⊆ OBJS ensures that all the periods are treated as world objects; this simplifies the semantics of top.
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fcons is a function CONS → OBJS. The notation D → R denotes a function with domain D and range R. fcons specifies which world object each constant denotes. In the airport domain, fcons would map the constant gate2 to a gate object, and ba737 to a flight object. fpfuns is a function that maps each pair π, n, where π ∈ PFUNS and n ∈ {1, 2, 3, . . . }, to another function (OBJS)n → pow(PERIODS). pow(S) denotes the powerset of S, i.e., the set of all subsets of S. (OBJS)n is the n-ary cartesian product OBJS × OBJS × · · · × OBJS. That is, for every π ∈ PFUNS and each n ∈ {1, 2, 3, . . . }, fpfuns (π, n) is a function that maps each n-tuple of elements of OBJS to a set of periods (an element of pow(PERIODS)). Intuitively, if τ1 , τ2 , . . . , τn are top terms denoting the world objects o1 , o2 , . . . , on , then fpfuns (π, n)(o1 , o2 , . . . , on ) is the set of the maximal periods where the situation represented by π(τ1 , τ2 , . . . , τn ) is true. For example, if the constant ba737 denotes a flight-object o1 , gate2 denotes a gate object o2 , and be at(ba737, gate2) represents the situation whereby flight o1 is located at gate o2 , then fpfuns (be at, 2)(o1 , o2 ) will be the set that contains all the maximal periods where flight o1 is located at gate o2 . For every π ∈ PFUNS, n ∈ {1, 2, 3, . . . }, and o1 , . . . , on ∈ (OBJS)n , it must be the case that: if p1 , p2 ∈ fpfuns (π, n)(o1 , . . . , on ) and p1 ∪ p2 ∈ PERIODS, then p1 = p2 . This ensures that no two different periods p1 , p2 in fpfuns (π, n)(o1 , . . . , on ) overlap or are adjacent, because if they overlap or they are adjacent, then their union is also a period, and then it must be true that p1 = p2 . Intuitively, if p1 and p2 overlap or are adjacent, we want fpfuns (π, n)(o1 , . . . , on ) to contain their union p1 ∪ p2 instead of p1 and p2 . fculms is a function that maps each pair π, n, where π ∈ PFUNS and n ∈ {1, 2, 3, . . . }, to another function (OBJS)n → {T, F}. T and F are the two truth values. That is, for every π ∈ PFUNS and n ∈ {1, 2, 3, . . . }, fculms (π, n) is a function that maps each n-tuple of OBJSn to T or F. fculms is consulted only for predicates that represent actions or changes that have inherent climaxes. If π(τ1 , . . . , τn ) represents such an action or change, and τ1 , . . . , τn denote the world objects o1 , . . . , on , then fpfuns (π, n)(o1 , . . . , on ) is the set of maximal periods where the action or change is ongoing. fculms (π, n)(o1 , . . . , on ) shows whether or not the climax is reached at the end of the latest maximal period. For example, if the constant j adams denotes a person o1 , bridge2 denotes an object o2 , and building(j adams, ba737) represents the situation whereby o1 is building o2 , then fpfuns (building, 2)(o1 , o2 ) is the set of all maximal periods
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where o1 is building o2 . fculms (building, 2)(o1 , o2 ) will be T if the building is completed at the end-point of the latest maximal period, and F otherwise. The role of fculms will become clearer in subsequent sections. fgparts is a function that maps each element of GPARTS to a gappy partitioning (Section 3.2). More formally, a gappy partitioning is a subset S of PERIODS, such that for every p1 , p2 ∈ S, p1 ∩ p2 = ∅ and p∈S p = PTS. Similarly, fcparts is a function that maps each element of CPARTS to a complete partitioning. A complete partitioning is a subset S of PERIODS, such that for every p1 , p2 ∈ S, p1 ∩p2 = ∅ and p∈S p = PTS. For example, fgparts (mondayg ) could be the gappy partitioning of all Monday-periods, and fcparts (dayc ) the complete partitioning of all day-periods.
. Variable assignment A variable assignment with respect to (w.r.t.) a top model M is a function g : VARS → OBJS. That is, g assigns a world object to each variable. GM , or simply G, is the set of all possible variable assignments w.r.t. M, i.e., the set of all functions VARS → OBJS. β If g ∈ G, β ∈ VARS, and o ∈ OBJS, then go is the variable assignβ ment defined as follows: go (β) = o, and for every β ∈ VARS with β = β, β go (β ) = g(β ).
. Denotation of a TOP expression As already mentioned, top formulae, and generally top expressions, are evaluated with respect to three times: speech time (st), event time (et), and localisation time (lt). More formally, st ∈ PTS, et ∈ PERIODS, and lt ∈ PERIODS*. Intuitively, st is the time-point where the English question is submitted to the nlitdb; et is a period, not necessarily maximal, where the situation represented by the top expression takes place; and lt can be thought of as a temporal window, within which et must be located. When computing the denotation of a top expression, lt is initially set to PTS. That is, the temporal window covers the whole time-axis, and et is allowed to be located anywhere. Various operators, however, may narrow down lt, imposing constraints on where et can be placed. The denotation of a top expression ξ w.r.t. a model M, st, et, lt, and a variable assignment g is written ξM,st,et,lt,g or simply ξst,et,lt,g . When the de-
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notation does not depend on st, et, and lt, the notation ξM,g , or simply ξg , will be used.
Denotation of terms and atomic formulae w.r.t. M, st, et, lt, g. The denotations of top expressions w.r.t. M, st, et, lt, and g are defined recursively, starting with the denotations of terms and atomic formulae, which are defined below. – – –
If κ ∈ CONS, then κg = fcons (κ). If β ∈ VARS, then βg = g(β). If φ ∈ YNFORMS, then φst,et,lt,g ∈ {T, F}.
The general rule above means that with yes/no formulae, we only need to define when the denotation is T; in all other cases the denotation is F. – –
If φ1 , φ2 ∈ YNFORMS, then φ1 ∧ φ2 st,et,lt,g = T iff φ1 st,et,lt,g = T and φ2 st,et,lt,g = T. If σ ∈ PARTS, β ∈ VARS, and νord ∈ {. . . , –3, –2, –1, 0}, then Part[σ, β, νord ]g is T iff all the following hold. Below f = fcparts if σ ∈ CPARTS, and f = fgparts if σ ∈ GPARTS: – g(β) ∈ f (σ). – If νord = 0, then st ∈ g(β). – If νord ≤ –1, then there are exactly –νord – 1 elements in the set: {p ∈ f (σ) | maxpt(g(β)) ≺ minpt(p) and maxpt(p) ≺ st}
That is, if νord = 0, then β must denote the current period of the partitioning. If νord ≤ –1, β must denote the –νord -th period of the partitioning that is completely situated before the speech time. For example, if νord = –4, then β must denote the 4th period which is completely situated before st; that is, there must be –νord – 1 = 3 periods in the partitioning that fall completely between the end of the period of β and st. If fcparts (dayc ) is the partitioning of all day-periods, then Part[dayc , β, 0]g is T iff g(β) covers exactly the whole current day; this captures the meaning of today. Similarly, Part[dayc , β, –1]g is T iff g(β) covers exactly the whole previous day; the meaning of yesterday. The definition of Part could be extended to allow positive values as its third argument, to express tomorrow, next January, etc. – –
If σ ∈ PARTS and β ∈ VARS, then Part[σ, β]g = T iff g(β) ∈ f (σ), where f as above. If π ∈ PFUNS and τ1 , . . . , τn ∈ TERMS, then π(τ1 , . . . , τn )st,et,lt,g is T iff et lt and for some pmxl ∈ fpfuns (π, n)(τ1 g , τ2 g , . . . , τn g ), et pmxl .
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That is, for the denotation of a predicate to be T, et must fall within lt, and et must be a subperiod of a maximal period where the situation described by the predicate holds. It is easy to prove that the definition above causes all top predicates to be homogeneous. A top formula is homogeneous iff for every st ∈ PTS, et ∈ PERIODS, lt ∈ PERIODS*, and g ∈ G, the following implication holds:
if et et and φst,et,lt,g = T, then φst,et ,lt,g = T. Intuitively, if a predicate is true at some et, then it is also true at any subperiod et of et. Although top predicates are homogeneous, more complex formulae are not always homogeneous. Various versions of homogeneity have been used by Allen (1984), Lascarides (1988), Richards et al. (1989), Kent (1993), Pratt and Bree (1995), and others. The term ‘homogeneity’ is also used in the temporal databases literature, but with a completely different meaning (Jensen et al. 1998).
Denotation of wh-formula w.r.t. M, st, et, lt, g. The denotation of a whformula w.r.t. M, st, et, lt, and g is defined below, where it is assumed that β1 , . . . , βn ∈ VARS and φ ∈ YNFORMS. –
?β1 . . . ?βn φst,et,lt,g = {g(β1 ), . . . , g(βn ) | φst,et,lt,g = T}
That is, if φst,et,lt,g = T, then ?β1 . . . ?βn φst,et,lt,g is a one-element set: it contains one tuple that holds the world-objects assigned to β1 , . . . , βn by g. Otherwise, ?β1 . . . ?βn φst,et,lt,g is the empty set. –
?mxl β1 ?β2 . . . ?βn φst,et,lt,g = {g(β1 ), g(β2 ), . . . , g(βn ) | φst,et,lt,g = T and for no et ∈ PERIODS and g ∈ G is it true that φst,et ,lt,g = T, g(β1 ) g (β1 ), g(β2 ) = g (β2 ), . . . , g(βn ) = g (βn )}
The denotation ?mxl β1 ?β2 . . . ?βn φst,et,lt,g is either a one-element set, that contains a tuple holding the world-objects g(β1 ), g(β2 ), . . . , g(βn ), or the empty set. The tuple contains the values assigned to β1 , β2 , . . . , βn by g, if these values satisfy φ, and there is no other et and variable assignment g that assigns the same values to β2 , . . . , βn and a superperiod of g(β1 ) to β1 , while still satisfying φ. That is, it must not be possible to extend any further the period assigned to β1 by g, preserving at the same time the values assigned to β2 , . . . , βn , and satisfying φ. Otherwise, the denotation of ?mxl β1 ?β2 . . . ?βn φ is the empty set.
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The syntax of top (Section 3.2) requires β1 to appear at least once within φ as the first argument of a Past, Perf , At, Before, After, or Ntense operator, or as the second argument of a Part operator. The semantics of these operators require variables occurring at these positions to denote periods. Hence, variable assignments g that do not assign a period to β1 will never satisfy φ, and no tuples for these variable assignments will be included in ?mxl β1 ?β2 . . . ?βn φst,et,lt,g . The denotations w.r.t. M, st, et, lt, and g of other top expressions will be defined in later sections.
Denotation w.r.t. M, st. We have so far considered the denotations of top expressions with respect to M, st, et, lt, and g. We will now define the denotations of top expressions with respect to only M and st. The denotation w.r.t. M and st is similar to the denotation w.r.t. M, st, et, lt, g, except that there is an implicit existential quantification over all g ∈ G and et ∈ PERIODS, and lt is set to PTS, i.e., the whole time-axis. The denotation of φ w.r.t. M, st, written φM,st or simply φst , is defined only for top formulae: –
If φ ∈ YNFORMS, then φst =
–
– T, if for some g ∈ G and et ∈ PERIODS, φst,et,PTS,g = T, – F, otherwise If φ ∈ WHFORMS, then φst = g∈G, et∈PERIODS φst,et,PTS,g .
Each question will be mapped to a top formula φ. (If the question is ambiguous, multiple formulae will be generated, one for each reading.) φst specifies what the nlitdb’s answer should report. When φ ∈ YNFORMS, φst = T, i.e., the answer should be affirmative, if for some assignment to the variables of φ and for some event time, φ is satisfied; otherwise φst = F, and the answer should be negative. The localisation time is set to PTS, the whole timeaxis, to reflect the fact that initially there is no restriction on where et may be located. As already mentioned, however, when computing the denotations of the subformulae of φ, temporal operators may narrow down lt, placing restrictions on et. In the case where φ ∈ WHFORMS, i.e., when φ =?β1 . . . ?βn φ or φ =?mxl β1 . . . ?βn φ with φ ∈ YNFORMS, φst is the union of all φst,et,PTS,g , for every g ∈ G and et ∈ PERIODS. For each g and et, φst,et,PTS,g is either an empty set or a one-element set containing a tuple that holds values of β1 , . . . , βn that satisfy φ ; β1 must also be maximal if φ ∈ WHFORMS2 . Hence, φst , the union of all φst,et,PTS,g , is the set of all the tuples that hold values of
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β1 , . . . , βn that satisfy φ . The answer should report these tuples to the user, or be a message like “No answer found” if φst = ∅.
. The Pres operator The Pres operator is used to express the simple present and present continuous. For φ ∈ YNFORMS: –
Pres[φ]st,et,lt,g = T, iff st ∈ et and φst,et,lt,g = T.
For example, (3.33) is represented as (3.34). Let us assume that the only maximal periods where BA737 is at gate 2 are pmxl1 and pmxl2 , i.e., (3.35) holds (Section 3.4). Let us also assume that (3.33) is submitted at a time-point st1 , such that (3.36) holds (Figure 3.1). (3.33) (3.34) (3.35) (3.36)
Is BA737 at gate 2? Pres[be at(ba737, gate2)] fpfuns (be at, 2)(fcons (ba737), fcons (gate2)) = {pmxl1 , pmxl2 } st1 ∈ pmxl2
The answer to (3.33) will be affirmative iff (3.37) is T; and (3.37) is T iff for some g ∈ G and et ∈ PERIODS, (3.38) holds (Section 3.6). (3.37) Pres[be at(ba737, gate2)]st1 (3.38) Pres[be at(ba737, gate2)]st1 ,et,PTS,g = T
By the definition of Pres, (3.38) holds iff both (3.39) and (3.40) hold. (3.39) st1 ∈ et (3.40) be at(ba737, gate2)st1 ,et,PTS,g = T
By the definitions of π(τ1 , . . . , τn )st,et,lt,g and κg (Section 3.6), (3.40) holds iff for some pmxl , (3.41)–(3.43) hold. (3.41) et PTS pmxl1
pmxl2 et st2
Figure 3.1 The semantics of the Pres operator
st1
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(3.42) pmxl ∈ fpfuns (be at, 2)(fcons (ba737), fcons (gate2)) (3.43) et pmxl
By (3.35), (3.42) is equivalent to (3.44). (3.44) pmxl ∈ {pmxl1 , pmxl2 }
The answer to (3.33), then, will be affirmative iff for some et ∈ PERIODS and some pmxl , (3.39), (3.41), (3.43), and (3.44) hold. They all hold for pmxl = pmxl2 and et any subperiod of pmxl2 that contains st1 (Figure 3.1). Hence, the answer to (3.33) will be affirmative, as one would expect. In contrast, if the question is submitted at an st2 that falls outside pmxl1 and pmxl2 (Figure 3.1), then the answer will be negative, because in that case there is no subperiod et of pmxl1 or pmxl2 that contains st2 . The present continuous is expressed similarly. For example, the reading of (3.45) where Airserve is actually servicing BA737 at the present moment is expressed as (3.46). Unlike proposals by Dowty (1977), Lascarides (1988), Crouch and Pulman (1993), and others, progressive forms do not introduce any progressive operator in top expressions. This will be discussed further when defining the semantics of the Culm operator. (3.45) Airserve is (actually) servicing BA737. (3.46) Pres[servicing(airserve, ba737)]
The habitual (3.47) is represented using a different predicate functor from that of (3.46), as in (3.48). (3.45) is taken to involve the non-habitual homonym of to service, while (3.47) is taken to involve the habitual one (Section 2.3). As will be explained in Chapter 4, the two homonyms introduce different predicate functors. (3.47) Airserve (habitually) services BA737. (3.48) Pres[hab server of (airserve, ba737)]
top’s Pres operator is similar to that of Pirie et al. (1990). The main difference is that the Pres operator of Pirie et al. does not require st to fall within et. Instead, it narrows lt to start at or after st. This, in combination with the requirement et lt, requires et to start at or after st. Using this version of Pres in (3.34) causes the answer to be affirmative if (3.33) is submitted at st2 (Figure 3.1), i.e., at a point where BA737 is not at gate 2, because there is an et at which BA737 is at gate 2 (e.g., the et of Figure 3.1), and this et starts after st2 . This version of Pres was adopted by Pirie et al. to cope with sentences like ‘Who in-
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spects BA737 tomorrow?’, where the simple present refers to a future inspection (Section 2.5.1), and et must be allowed to start after st. To restrict the semantics of their Pres operator when it is over-permissive, Pirie et al. employ a post-processing mechanism, which is invoked after the English sentence is translated into meaning representation language. If the Pres is introduced by a state verb, excluding progressive states, and the verb is not modified by a temporal adverbial, then et is set to {st}. For example, in J. Adams is at site 2 where the verb is a lexical state, the mechanism causes et to be set to {st}, which correctly requires J. Adams to be at site 2 at st. In J. Adams is at site 2 tomorrow, where the state verb is modified by a temporal adverbial, the post-processing has no effect, and et is allowed to start at or after st. In J. Adams is inspecting site 2, where the verb is a progressive state, the post-processing has again no effect, and et can start at or after st. The rationale in this case is that et cannot be set to {st}, because there is a reading where the present continuous refers to a future inspection (Section 2.5.3). For the purposes of this book, where future readings are ignored, top’s Pres operator is adequate. If, however, future readings were to be supported, a more permissive Pres operator, like that of Pirie et al., might have to be adopted.
. The Past operator The Past operator is used when expressing the simple past, the past continuous, the past perfect, and the present perfect. top’s Past operator is essentially the same as that of Pirie et al. (1990). For φ ∈ YNFORMS and β ∈ VARS: –
Past[β, φ]st,et,lt,g = T, iff g(β) = et and φst,et,lt∩[tfirst ,st),g = T.
The Past operator narrows the localisation time, forcing it to end before st. When computing the denotation of φ, et will be required to be a subperiod of the localisation time. Hence, et will be required to end before st. β is used as a pointer to et: its value is required to be et. β is useful in formulae that contain Ntense operators, to be discussed in subsequent sections. It is also useful in time-asking questions, where et has to be reported. For example, (3.49) is represented as (3.50). The latter reports the maximal ets that end before st, such that gate 2 is open throughout et. (3.49) When was gate 2 open? (3.50) ?mxl ev Past[ev , open(gate2)]
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. Progressives, non-progressives and the Culm operator We now examine in more detail how top represents the simple past and the past continuous. We start from verbs whose base forms are culminating activities, like to inspect in the airport domain. The past continuous (3.51) is represented as (3.52). (3.51) Was J. Adams inspecting BA737? (3.52) Past[ev , inspecting(ja, ba737)]
Let us assume that the inspection of BA737 by J. Adams started at the beginning of pmxl1 (Figure 3.2), that it stopped temporarily at the end of pmxl1 , that it was resumed at the beginning of pmxl2 , and that it was completed at the end of pmxl2 . Let us also assume that there is no other time where J. Adams is inspecting BA737. Then, (3.53) and (3.54) hold. (3.53) fpfuns (inspecting, 2)(fcons (ja), fcons (ba737)) = {pmxl1 , pmxl2 } (3.54) fculms (inspecting, 2)(fcons (ja), fcons (ba737)) = T
From the top definitions so far, it follows that (3.55) is T iff there is an et that is a subperiod of pmxl1 or pmxl2 and that ends before st. (3.55) Past[ev , inspecting(ja, ba737)]st
If (3.51) is submitted at the st1 or st2 of Figure 3.2, then (3.55) is T, because in both cases there is an et, for example the et1 of Figure 3.2, that ends before st1 and st2 , and that is a subperiod of pmxl1 . In contrast, if the question is submitted at st3 , (3.55) is F, because in this case there is no subperiod of pmxl1 or pmxl2 that ends before st3 . This is correct: at st1 or st2 the answer to (3.51) is affirmative, because J. Adams has already spent some time inspecting BA737; in contrast, at st3 J. Adams has not yet spent any time inspecting BA737, and the answer is negative. Let us now consider the simple past (3.56). We want the answer to be affirmative if (3.56) is submitted at st1 or any other time-point after the end of pmxl2 , et2 inspecting pmxl1 st3
et1
inspecting pmxl2
st2
Figure 3.2 The semantics of the Past operator
inspection completed
st1
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but not if it is submitted at st2 or any other time-point before the end of pmxl2 , because at st2 J. Adams has not yet completed the inspection. (3.56) cannot be represented as (3.52), because this would cause the answer to be affirmative if the question is submitted at st2 . Instead, (3.56) is represented as (3.57). The same predicate inspecting(ja, ba737) of (3.52) is used, but an additional Culm operator is inserted. (3.56) Did J. Adams inspect BA737? (3.57) Past[ev , Culm[inspecting(ja, ba737)]]
Intuitively, the Culm operator requires the event time to be the et2 of Figure 3.2, i.e., to cover the whole time from the point where the inspection starts to the point where the inspection is completed. If the inspection is never completed, the Culm operator causes the denotation of (3.57) to be F. Combined with the Past operator, the Culm operator causes the answer to be affirmative if (3.56) is submitted at st1 , because et2 ends before st1 , and negative if the question is submitted at st2 , because et2 does not end before st2 . More formally, for π ∈ PFUNS and τ1 , . . . , τn ∈ TERMS: –
Culm[π(τ1 , . . . , τn )]st,et,lt,g = T, iff et lt, fculms (π, n)(τ1 g , . . . , τn g ) = T, S = ∅, and et = [minpt(S), maxpt(S)], where S = p∈fpfuns (π,n)(τ1 g ,...,τn g ) p.
The fculms (π)(τ1 g , . . . , τn g ) = T means that the change or action of π(τ1 , . . . , τn ) must reach its climax at the latest time-point where it is ongoing. The et = [minpt(S), maxpt(S)] requires et to start at the first time-point where the change or action is ongoing, and to end at the latest point. Let us now check formally that the denotation (3.58) of (3.57) is in order. (3.58) is T iff for some g ∈ G and et ∈ PERIODS, (3.59) holds. (3.58) Past[ev , Culm[inspecting(ja, ba737)]]st (3.59) Past[ev , Culm[inspecting(ja, ba737)]]st,et,PTS,g = T
By the definition of Past, (3.59) holds iff (3.60) and (3.61) hold. (3.60) g(ev ) = et (3.61) Culm[inspecting(ja, ba737)]st,et,[tfirst ,st),g = T
By the definition of Culm, (3.61) holds iff (3.62)–(3.66) hold. (3.62) et [tfirst , st) (3.63) fculms (inspecting, 2)(fcons (ja), fcons (ba737)) = T (3.64) S =
∅
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(3.65) et = [minpt(S), maxpt(S)] (3.66) S = p∈fpfuns (inspecting,2)(fcons (ja),fcons(ba737)) p
By (3.53), and assuming that maxpt(pmxl1 ) ≺ minpt(pmxl2 ) as in Figure 3.2, (3.64)–(3.66) are equivalent to (3.67)–(3.68). (3.67) holds, because the union of two periods is never the empty set. (3.67) pmxl1 ∪ pmxl2 = ∅ (3.68) et = [minpt(pmxl1 ), maxpt(pmxl2 )]
(3.63) is the same as (3.54), which was assumed to hold. Hence, (3.58) is T iff for some g ∈ G and et ∈ PTS, (3.60), (3.62), and (3.68) hold. Let et2 = [minpt(pmxl1 ), maxpt(pmxl2 )], as in Figure 3.2, and let us assume that (3.56) is submitted at an st that follows the end of et2 ; for example, st1 in Figure 3.2. For et = et2 , (3.62) and (3.68) are satisfied. (3.60) is also satisfied by choosing g = g1 , where g1 as below. Hence, the answer to (3.56) will be affirmative, as required. g1 (β) =
et2 o
if β = ev otherwise, where o is an arbitrary element of OBJS
In contrast, if (3.56) is submitted before the end of et2 , for example at st2 or st3 in Figure 3.2, then the answer will be negative, because there is no et that satisfies both (3.62) and (3.68). In the case of verbs whose base forms are processes, states, or points, the simple past does not introduce a Culm operator. In this case, when both the simple past and the past continuous are possible, they are represented using the same top formula. For example, in the airport domain where to circle is a process, both (3.69) and (3.70) are represented as (3.71). (3.69) Was BA737 circling? (3.70) Did BA737 circle? (3.71) Past[ev , circling(ba737)]
The top definitions above imply that the denotation of (3.71) w.r.t. st is T, i.e., the answer to (3.69) and (3.70) is affirmative, iff there is an et which is a subperiod of a maximal period where BA737 was circling, and et ends before st. That is, the answer is affirmative iff BA737 was circling at some time before st. There is no requirement for the climax to have been reached. The reader will have noticed that in the case of verbs whose base forms are culminating activities, the non-progressive form, in this case the simple past,
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is represented by adding a Culm operator to the top expression that represents the corresponding progressive form, here the past continuous. For example, assuming that to build is a culminating activity, (3.72) is represented as (3.73), and (3.74) as (3.75). (3.72) (3.73) (3.74) (3.75)
Housecorp was building bridge 2. Past[ev , building(housecorp, bridge2)] Housecorp built bridge 2. Past[ev , Culm[building(housecorp, bridge2)]]
A similar approach is adopted by Parsons (1989). In contrast, Dotwy (1977), Lascarides (1988), Pirie et al. (1990), Kamp and Reyle (1993), and others represent progressive forms by adding a ‘progressive’ operator to the expressions that represent the non-progressive forms. For example, ignoring some details, Pirie et al. represent (3.72) and (3.74) as (3.76) and (3.77), respectively. (3.76) Past[ev , Prog[build(housecorp, bridge2)]] (3.77) Past[ev , build(housecorp, bridge2)]
In (3.77), the semantics that Pirie et al. assign to build(housecorp, bridge2) require et to cover the whole building of the bridge, from its beginning to the point where the building is complete. (In contrast, the semantics of top require et to be simply a period throughout which Housecorp was building bridge 2.) The Past operator of (3.77) requires et to end before st. Hence, the answer to (3.74) is affirmative iff the building was completed before st. In (3.76), the semantics that Pirie et al. assign to Prog require et to be a subperiod of another period et that covers the entire building, from start to completion, as in Figure 3.3. The Past operator of (3.76) requires et to end before st. If, for example, (3.72) is submitted at an st that falls between the end of et and the end of et (Figure 3.3), the answer will be affirmative. This is correct, because at that st Housecorp has already been building the bridge for some time, although the bridge is not yet complete.
et
building complete
et¢ building started
Figure 3.3 A flawed Prog operator
st
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The Prog of Pirie et al., however, has a flaw (Crouch & Pulman 1993): (3.76) implies that there is a period et , such that the building is completed at the end of et ; i.e., according to (3.76) the building was or will be necessarily completed at some time-point. This does not capture correctly the semantics of (3.72), which carries no implication that the building was or will ever be completed. top’s representation of (3.72), i.e., (3.73), does not suffer from this problem, because it does not assume that the building is ever completed. To overcome similar problems with Prog operators, ‘branching’ models of time or ‘possible worlds’ have been employed (Dowty 1977; McDermott 1982; Mays 1986; Kent 1993); see also Lascarides (1988) for criticism of possibleworlds approaches. Branching time and possible worlds, however, seem unnecessarily complex for the purposes of this book.
. The At, Before and After operators The At, Before, and After operators are used to express punctual adverbials, period adverbials, and subordinate clauses introduced by while, before, and after (Sections 2.9 and 2.10). For φ, φ1 , φ2 ∈ YNFORMS and τ ∈ TERMS: g – At[τ, φ]st,et,lt,g = T, iff τg ∈ PERIODS and φst,et,lt∩τ ,g = T. –
At[φ1 , φ2 ]st,et,lt,g = T, iff for some et et ∈ mxlpers({e ∈ PERIODS | φ1 st,e,PTS,g = T}) and φ2 st,et,lt∩et ,g = T.
In the first form of the At operator, τ must denote a period. The localisation time is narrowed to the intersection of the original lt with the period of τ. In the second form of the At operator, the localisation time of φ2 is narrowed to the intersection of the original lt with a maximal event time period et where φ1 holds. For example, (3.78) is represented as (3.79). In (3.79), lt initially covers the whole time-axis. Assuming that the constant 25/9/1999 denotes the obvious period, the At operator causes lt to become the period that covers exactly 25/9/1999. The Past operator then forces lt to end before st. If 25/9/1999 is entirely in the past, the Past operator has no effect. The answer to (3.78) is affirmative iff it is possible to find an et that is a subperiod of the resulting lt, such that tank 2 was empty during et. (3.78) Was tank 2 empty (some time) on 25/9/1999? (3.79) At[25/9/1999, Past[ev , empty(tank2)]]
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If (3.78) is submitted before 25/9/1999, the nlitdb’s answer will be negative, because the At and Past operators cause lt to become the empty set, and hence it is impossible to find a subperiod et of lt where tank 2 is empty. This is not entirely satisfactory. (3.78) is unacceptable, if uttered before 25/9/95, and the system should warn the user about this. The unacceptability of (3.78) in this case seems related to the unacceptability of (3.80), which would be represented as (3.81). (The definition of Part would have to be extended to allow positive values of its third argument.) (3.80) *Was tank 2 empty tomorrow? (3.81) Part[dayc , tomv , 1] ∧ At[tomv , Past[ev , empty(tank2)]]
In both cases, the combination of the simple past and the adverbial causes lt to become the empty set. In (3.81), for example, tomv denotes the period that covers exactly the day after st. The At and Past operators set lt to the intersection of that period with [tfirst , st). The two periods do not overlap, i.e., lt = ∅; hence, it is impossible to find a subperiod et of lt. This causes the answer to be always negative, regardless of what happens in the world, i.e., regardless of when tank 2 is empty. It may be the case that the questions sound unacceptable, because people, using a concept similar to top’s lt, realise that the answers can never be affirmative. This suggests that the nlitdb should generate a cooperative response when lt = ∅, explaining that the question is problematic. This would be similar to the ‘overlap rule’ of Harper (1986) and the ‘non-triviality constraint’ of Kamp and Reyle (1993: 653). As this book does not consider cooperative responses (Section 1.2), mechanisms of this type will not be explored further. Moving to further examples, (3.82) and (3.84) are represented as (3.83) and (3.85), respectively. Unlike the on 25/9/1999 of (3.78), which is represented using a constant (25/9/1999), the on Monday of (3.82) is represented using a variable (monv ) that ranges over the periods of the partitioning of Mondayperiods. Similarly, the at 5:00 pm of (3.84) is represented using a variable (fvv ) that ranges over the 5:00 pm minute-periods. (3.82) (3.83) (3.84) (3.85)
Was tank 2 empty on Monday? Part[mondayg , monv ] ∧ At[monv , Past[ev , empty(tank2)]] Was tank 2 empty on Monday at 5:00 pm? Part[mondayg , monv ] ∧ Part[5:00pmg , fvv ] ∧ At[monv , At[fvv , Past[ev , empty(tank2)]]]
(3.83) requires tank 2 to have been empty at some past et that falls within some Monday. No attempt is made to determine exactly which Monday the user has in mind (Section 2.12). Similarly, (3.85) requires tank 2 to have been empty at
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some past et that falls within the intersection of some 5:00 pm minute-period with some Monday-period. Assuming that to inspect is a culminating activity, as in the airport domain, the reading of (3.86) that requires the inspection to have both started and been completed within the previous day (Section 2.9.2) is represented as (3.87). The Culm requires et to cover exactly the whole inspection, from its beginning to its completion. The Past requires et to end before st, and the At requires et to fall within the day before st. (3.86) Did J. Adams inspect BA737 yesterday? (3.87) Part[dayc , yv , –1] ∧ At[yv , Past[ev , Culm[inspecting(ja, ba737)]]]
In contrast, (3.88) is represented as (3.89). In this case, et must be simply a subperiod of a maximal period where J. Adams was inspecting BA737, and it must be located within the previous day. (3.88) Was J. Adams inspecting BA737 yesterday? (3.89) Part[dayc , yv , –1] ∧ At[yv , Past[ev , inspecting(ja, ba737)]]
Finally, (3.90) is represented as (3.91), which requires BA737 to have been circling at some past period e2v , that falls within some past maximal period e1v where gate 2 was open. (3.90) Did BA737 circle while gate 2 was open? (3.91) At[Past[e1v , open(gate2)], Past[e2v , circling(ba737)]]
The Before and After operators are similar. They are used to express adverbials and subordinate clauses introduced by before and after. For φ, φ1 , φ2 ∈ YNFORMS and τ ∈ TERMS: – –
– –
Before[τ, φ]st,et,lt,g = T, iff τg ∈ PERIODS and g φst,et,lt∩[tfirst ,minpt(τ )),g = T. Before[φ1 , φ2 ]st,et,lt,g = T, iff for some et et ∈ mxlpers({e ∈ PERIODS | φ1 st,e,PTS,g = T}) and φ2 st,et,lt∩[tfirst ,minpt(et )),g = T. After[τ, φ]st,et,lt,g = T, iff τg ∈ PERIODS and g φst,et,lt∩(maxpt(τ ),tlast ],g = T. After[φ1 , φ2 ]st,et,lt,g = T, iff for some et et ∈ mxlpers({e ∈ PERIODS | φ1 st,e,PTS,g = T}) and φ2 st,et,lt∩(maxpt(et ),tlast ],g = T.
In the first form of the Before operator, τ must denote a period, and the localisation time is required to end before the beginning of τ’s period. In the second
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form of the Before operator, the localisation time of φ2 is required to end before the beginning of a maximal event time period et where φ1 holds. The After operator is similar. For example, (3.92) is expressed as (3.93). The reading of (3.94) that requires BA737 to have departed after the end of a maximal period where the emergency system was in operation is expressed as (3.95). It is assumed here that to depart is a point, as in the airport domain. (3.92) (3.93) (3.94) (3.95)
Was tank 2 empty before 25/9/1999? Before[25/9/1999, Past[ev , empty(tank2)]] BA737 departed after the emergency system was in operation. After[Past[e1v , in oper(emerg sys)], Past[e2v , depart(ba737)]]
(3.94) also has a reading where BA737 must have departed after the emergency system started to be in operation (Section 2.10.2). To express this reading, an additional Begin operator is needed. We will return to this reading when defining the semantics of the Begin operator. top’s At, Before, and After operators are similar to those of Pirie et al. (1990). The operators of Pirie et al., however, do not narrow lt as in top. Instead, they place directly restrictions on et. For example, ignoring some details, the After[φ1 , φ2 ] operator of Pirie et al. requires φ2 to hold at an event time et2 that follows an et1 where φ1 holds; both et1 and et2 must fall within lt. Instead, top’s After[φ1 , φ2 ] requires et1 to be a maximal period where φ1 holds, not necessarily within the original lt, and evaluates φ2 with respect to a narrowed lt, which is the intersection of the original lt with et1 . In most cases, both approaches lead to similar results. However, top’s approach, i.e., narrowing lt, is advantageous in sentences like (3.96) when expressing the durative reading, whereby the tank was empty throughout 26/9/1999 (Section 2.9.2). (3.96) Tank 2 was empty on 26/9/1999.
In these cases et must cover all the available time, i.e., all the time where the tense and the adverbial allow et to be placed. top’s lt captures this notion of available time. Hence, in top the durative reading can be expressed easily using an additional Fills operator that forces et to cover the whole lt; this will be discussed further in Section 3.11 below. This method cannot be used in the language of Pirie et al. Their Past operator narrows lt to the time-axis up to st, but their At operator does not narrow lt any further. Instead, it imposes a direct restriction on et. Hence, lt is left to be the time-axis up to st, and the durative reading cannot be captured by requiring et to be equal to lt.
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. The Fills operator Let us now define the Fills operator, that allows the durative reading of (3.96) to be captured. For φ ∈ YNFORMS: –
Fills[φ]st,et,lt,g = T, iff et = lt and φst,et,lt,g = T.
The Fills operator requires et to cover the entire lt, i.e., all the time where et is allowed to be placed. The durative reading of (3.96) can now be expressed as (3.97). In contrast, (3.98) captures the inclusive reading; the tank must have been empty simply at some part of 26/9/1999. (3.97) At[26/9/1999, Past[ev , Fills[empty(tank2)]]] (3.98) At[26/9/1999, Past[ev , empty(tank2)]]
Similarly, the reading of (3.99) whereby BA737 was at gate 2 throughout the entire inspection is captured by (3.100). In (3.101), the durative reading is that tank 2 was empty throughout the previous August; this is captured by (3.102). (3.99) BA737 was at gate 2 while J. Adams was inspecting UK160. (3.100) At[Past[e1v , inspecting(ja, uk160)], Past[e2v , Fills[be at(ba737, gate2)]]] (3.101) Tank 2 was empty in August last summer. (3.102) Part[august g , aug v ] ∧ Part[summerg , sumv , –1] ∧ At[aug v , At[sumv , Past[ev , Fills[empty(tank2)]]]]
When both the durative and the inclusive readings are possible, an nlitdb could paraphrase both and ask the user to select one of them, or it could provide answers to both readings, indicating which answer corresponds to which reading. As discussed in Section 2.9.2, however, determining exactly when the durative readings are possible is a difficult task. For simplicity, only inclusive readings will be considered in the rest of this book.
. The Begin and End operators The Begin and End operators are used to refer to the time-points where a situation starts or ends. For φ ∈ YNFORMS: –
Begin[φ]st,et,lt,g = T, iff et ∈ mxlpers({e ∈ PERIODS | φst,e,PTS,g = T}), et = {minpt(et )}, and et lt.
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–
End[φ]st,et,lt,g = T, iff et ∈ mxlpers({e ∈ PERIODS | φst,e,PTS,g = T}), et = {maxpt(et )}, and et lt.
Begin[φ] is true only at instantaneous event times et that are beginnings of maximal event times et where φ holds. The End operator is similar. The Begin and End operators can express to start, to stop, to begin, and to finish (Section 2.6). For example, (3.103) is expressed as (3.104). (3.103) Did T. Smith start to inspect BA737 before J. Adams finished inspecting UK160? (3.104) Before[Past[e1v , End[Culm[inspecting(ja, uk160)]]], Past[e2v , Begin[inspecting(ts, ba737)]]]
Intuitively, Culm[inspecting(ja, uk160)] refers to an event-time period that covers exactly an entire inspection of UK160 by J. Adams, from start to completion. End[Culm[inspecting(ja, uk160)]] refers to the completion point of the inspection. Begin[inspecting(ts, ba737)] refers to the beginning of an inspection of BA737 by T. Smith. (3.104) requires the beginning of T. Smith’s inspection to precede the completion point of J. Adams’ inspection, and both points to fall in the past. The reading of (3.94) (Section 3.10) that requires BA737 to have departed after the emergency system started to be in operation can now be expressed as (3.105). (3.105) After[Past[e1v , Begin[in operation(emerg sys)]], Past[e2v , depart(ba737)]]
. The Ntense operator The framework of this book allows noun phrases to refer either to the present or to the time of the verb tense (Section 2.11). In (3.106), for example, the sales manager can refer either to the current sales manager or to the 1991 sales manager. The two readings are represented using the Ntense operator, as in (3.107) and (3.108), respectively. (3.106) What was the salary of the sales manager in 1991? (3.107) ?slrv Ntense[now*, manager of (mgrv , sales)] ∧ At[1991, Past[ev , salary of (mgrv , slr v )]]
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(3.108) ?slrv Ntense[ev , manager of (mgrv , sales)] ∧ At[1991, Past[ev , salary of (mgrv , slr v )]]
Intuitively, (3.107) reports any slrv , such that slrv was the salary of mgrv at some past time ev that falls within 1991, and mgrv is the current manager of the sales department. In contrast, in (3.108) mgrv must be the manager of the sales department at ev . Notice that in (3.108) the first argument of the Ntense is the same as the first argument of the Past, which is a pointer to the past event time where salary of (mgrv , slrv ) is true (Section 3.8). top’s Ntense operator is borrowed from Crouch and Pulman (1993). For φ ∈ YNFORMS and β ∈ VARS : – –
Ntense[β, φ]st,et,lt,g = T, iff for some et ∈ PERIODS, it is true that g(β) = et and φst,et ,PTS,g = T. Ntense[now*, φ]st,et,lt,g = T, iff φst,{st},PTS,g = T.
Ntense evaluates φ with respect to a new event time et , which may be different from the original event time et that is used to evaluate the part of the formula outside the Ntense. Within the Ntense, the localisation time is reset to PTS, i.e., the whole time-axis, freeing et from restrictions imposed on the original et. If the first argument of Ntense is now*, the new event time is the instantaneous period that contains only st, i.e., the object to which the noun phrase refers must have at st the property described by φ. If the first argument of Ntense is a variable β, the new event time et can generally be any period, and β denotes et . In (3.108), however, β is the same as the first argument of the Past operator, which denotes the original et that the Past operator requires to be placed before st. This means that manager of (mgrv , sales) must hold at the same event time where salary of (mgrv , slrv ) holds, i.e., the person mgrv must be the sales manager at the same time where the salary of mgrv is slrv . If the first argument of the Ntense in (3.108) and the first argument of the Past were different variables, the answer would contain any 1991 salary of anybody who was, is, or will be the sales manager at any time. Using different variables in the two arguments would be useful in (3.109), where the preferred reading is that Prime Minister refers to the Prime Ministers of all times, a reading captured by (3.110). (3.109) Which Prime Ministers were born in Scotland? (3.110) ?pmv Ntense[e1v , pminister(pmv )] ∧ Past[e2v , birth in(pmv , scotland)]
The framework of this book, however, does not currently generate (3.110). (3.109) receives only two formulae, one for current Prime Ministers, and one
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for persons that were Prime Ministers at the time they were born. The latter reading is unlikely in this case. Questions like (3.111) and (3.113), where temporal adjectives specify explicitly the times of the noun phrases, can be represented as (3.112) and (3.114), respectively. In the rest of this book, however, we will not consider temporal adjectives other than current (Section 2.8). (3.111) What was the salary of the current sales manager in 1991? (3.112) ?slrv Ntense[now*, manager of (mgrv , sales)] ∧ At[1991, Past[ev , salary of (mgrv , slr v )]] (3.113) What was the salary of the 1988 sales manager in 1991? (3.114) ?slrv Ntense[e1v , At[1988, manager of (mgrv , sales)]] ∧ At[1991, Past[e2v , salary of (mgrv , slr v )]]
. The For operator The For operator will be used to express duration adverbials introduced by for and in (Sections 2.9.3 and 2.9.4). For σc ∈ CPARTS, νqty ∈ {1, 2, 3, . . . }, and φ ∈ YNFORMS: –
For[σc , νqty , φ]st,et,lt,g = T, iff φst,et,lt,g = T and for some p1 , p2 , . . . , pνqty ∈ fcparts (σc ), minpt(p1 ) = minpt(et), next(maxpt(p1 )) = minpt(p2 ), next(maxpt(p2 )) = minpt(p3 ), . . . , next(maxpt(pνqty –1 )) = minpt(pνqty ), and maxpt(pνqty ) = maxpt(et).
For[σc , νqty , φ] requires φ to be true at an event time period that is νqty σc periods long. For example, assuming that monthc denotes the partitioning of month-periods, i.e., the period that covers exactly the August of 1995, the period for September of 1995, etc., (3.115) can be expressed as (3.116). (3.115) Was tank 2 empty for three months? (3.116) For[monthc , 3, Past[ev , empty(tank2)]]
(3.116) requires an event time et to exist, such that et covers exactly three consecutive months, and tank 2 was empty throughout et. As noted in Section 2.9.3, for adverbials are sometimes used to specify the duration of a maximal period where a situation holds, or to refer to the total duration of possibly non-overlapping periods where some situation holds. These readings are
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not considered in this book, and hence we will not define top mechanisms to capture them. Expressions like one week, three months, two years, two hours, etc., are often used to specify durations of seven days, 3 × 30 days, 2 × 365 days, 2 × 60 minutes, etc., respectively. (3.116) expresses (3.115) if three months refers to calendar months; for example, from the beginning of a June to the end of the following August. If three months means 3 × 30 days, (3.117) has to be used instead. It is assumed here that dayc denotes the partitioning of day-periods, i.e., the period that covers exactly 26/9/1999, the period for 27/9/1999, etc. (3.117) For[dayc , 90, Past[ev , empty(tank2)]]
Assuming that to inspect is a culminating activity, as in the airport domain, (3.119) represents the reading of (3.118) where 42 minutes is the duration from the beginning of the inspection to the inspection’s completion (Section 2.9.4). (3.118) J. Adams inspected BA737 in 42 minutes. (3.119) For[minutec , 42, Past[ev , Culm[inspecting(ja, ba737)]]]
Unlike (3.118), (3.120) does not require the inspection to have been completed (Section 2.9.3). (3.120) is represented as (3.121), i.e., without the Culm operator. (3.120) J. Adams inspected BA737 for 42 minutes. (3.121) For[minutec , 42, Past[ev , inspecting(ja, ba737)]]
. The Perf operator The Perf operator is used when expressing the past perfect. For example, (3.122) is expressed as (3.123). The Perf operator could also be used in present perfect sentences; e.g., (3.124) would be represented as (3.125). In this book, however, the present perfect is taken to have the same meaning as the simple past (Section 2.5.4). Hence, (3.124) will be mapped to (3.127), the same formula that expresses (3.126). (3.122) (3.123) (3.124) (3.125) (3.126) (3.127)
BA737 had departed. Past[e1v , Perf [e2v , depart(ba737)]] BA737 has departed. Pres[Perf [ev , depart(ba737)]] BA737 departed. Past[ev , depart(ba737)]
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top’s Perf operator has been influenced by similar operators proposed by Dowty (1982), Richards et al. (1989), Pirie et al. (1990), and Crouch et al. (1993). For φ ∈ YNFORMS and β ∈ VARS: –
Perf [β, φ]st,et,lt,g = T, iff et lt and for some et ∈ PERIODS, it is true that g(β) = et , maxpt(et ) ≺ minpt(et), and φst,et ,PTS,g = T.
Perf [β, φ] holds at the event time et, only if et is preceded by a new event time et where φ holds (Figure 3.4). The original et must be a subperiod of lt. In contrast, et does not need to be a subperiod of lt, because the localisation time in φst,et ,PTS,g above is reset to PTS, the whole time-axis. The β argument is a pointer to et , as in Past[β, φ] (Section 3.8). Ignoring constraints imposed by lt, the et where Perf [β, φ] is true can be placed anywhere within the period that starts immediately after the end of et and extends up to tlast . The term consequent period was used in Section 2.9.1 to refer to this period. Using the Perf operator, the reading of (3.128) where the inspection happens at some time before, or possibly on, 27/9/1995 is expressed as (3.129). In this case, on 27/9/1995 provides a reference time; see Section 2.5.5. In contrast, the reading of (3.128) where the inspection happens on 27/9/1995 is expressed as (3.130). (3.128) J. Adams had inspected gate 2 on 27/9/1995. (3.129) At[27/9/1995, Past[e1v , Perf [e2v , Culm[inspecting(ja, g2)]]]] (3.130) Past[e1v , Perf [e2v , At[27/9/1995, Culm[inspecting(ja, g2)]]]]
Let us explore formally the denotations of (3.129) and (3.130). The denotation of (3.129) w.r.t. st is T iff for some et ∈ PERIODS and g ∈ G, (3.131) holds. (3.131) At[27/9/1995, Past[e1v , Perf [e2v , Culm[inspecting(ja, g2)]]]]st,et,PTS,g = T
Assuming that 27/9/1995 denotes the obvious period, by the definition of At, (3.131) holds iff (3.132) is true. (3.132) Past[e1v , Perf [e2v , Culm[inspecting(ja, g2)]]]st,et,fcons(27/9/1995),g = T lt j et¢
Figure 3.4 The semantics of the Perf operator
Perf[ev, j] et
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By the definition of Past, ignoring e1v which does not play any interesting role here, and assuming that st follows 27/9/1995, (3.132) becomes (3.133). (3.133) Perf [e2v , Culm[inspecting(ja, g2)]]st,et,fcons (27/9/1995),g = T
By the definition of Perf , ignoring e2v , (3.133) holds iff for some et ∈ PERIODS, (3.134)–(3.136) hold. (3.134) et fcons (27/9/1995) (3.135) maxpt(et ) ≺ minpt(et) (3.136) Culm[inspecting(ja, g2)]st,et ,PTS,g = T
By the definition of Culm, (3.136) holds iff (3.137)–(3.141) hold. (3.137) (3.138) (3.139) (3.140) (3.141)
et PTS fculms (inspecting, 2)(fcons (ja), fcons (g2)) = T S = p∈fpfuns (inspecting,2)(fcons(ja),fcons(g2)) p S = ∅ et = [minpt(S), maxpt(S)]
Let us assume that there is only one maximal period where J. Adams is inspecting BA737, and that the inspection is completed at the end of that period. Then, the S of (3.139) is that maximal period, and (3.138) and (3.140) hold. (3.141) requires et to be the same period as S, and (3.137) is satisfied. The denotation of (3.129) w.r.t. st, then, is T iff for some et, (3.134) and (3.135) hold, i.e., iff there is an et within 27/9/1995, such that et follows the period S = et that covers the entire inspection. The situation is depicted in Figure 3.5. In other words, 27/9/1995 must contain an et where the inspection has already been completed. Let us now consider (3.130). Its denotation w.r.t. st will be true iff for some et ∈ PERIODS and g ∈ G, (3.142) holds. (3.142) Past[e1v , Perf [e2v , At[27/9/1995, Culm[inspecting(ja, g2)]]]]st,et,PTS,g = T
By the definition of Past, ignoring again e1v and e2v which do not play any interesting role here, (3.142) holds iff (3.143) is T. S = et¢
et
st
27/9/1995
Figure 3.5 First reading of “J. Adams had inspected gate 2 on 27/9/1995”
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(3.143) Perf [e2v , At[27/9/1995, Culm[inspecting(ja, g2)]]]st,et,[tfirst ,st),g = T
By the definition of Perf , (3.143) is true iff for some et ∈ PERIODS, (3.144)– (3.146) hold. (3.144) et [tfirst , st) (3.145) maxpt(et ) ≺ minpt(et) (3.146) At[27/9/1995, Culm[inspecting(ja, g2)]]st,et ,PTS,g = T
By the definition of the At operator, (3.146) holds iff (3.147) holds.
(3.147) Culm[inspecting(ja, g2)]st,et ,fcons (27/9/1995),g = T
By the definition of Culm, (3.147) holds iff (3.148)–(3.152) are true. (3.148) (3.149) (3.150) (3.151) (3.152)
et fcons (27/9/1995) fculms (inspecting, 2)(fcons (ja), fcons (g2)) = T S = p∈fpfuns (inspecting,2)(fcons(ja),fcons(g2)) p S = ∅ et = [minpt(S), maxpt(S)]
Assuming again that there is only one maximal period where J. Adams is inspecting BA737, and that the inspection is completed at the end of the period, the S of (3.150) is that maximal period, and (3.149) and (3.151) hold. (3.152) sets et to S. The denotation of (3.130) w.r.t. st, then, is T iff for some et, (3.144), (3.145), and (3.148) hold. That is, there must be some past et that follows the period S = et of the entire inspection, and S = et must be located within 27/9/1995 (Figure 3.6). In other words, in this case the inspection must have been completed within 27/9/1995. In (3.153), where there are no temporal adverbials, the corresponding formula (3.154) requires some past et (pointed to by e1v ) to exist, such that et follows an et (pointed to by e2v ) that covers exactly the whole inspection of gate 2 by J. Adams, from start to completion. The net effect is that the inspection must have been completed in the past. S = et¢
et
st
27/9/1995
Figure 3.6 Second reading of “J. Adams had inspected gate 2 on 27/9/1995”
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The TOP meaning representation language
(3.153) J. Adams had inspected gate 2 (3.154) Past[e1v , Perf [e2v , Culm[inspecting(ja, g2)]]]
. Occurrence identifiers In this book, predicates introduced by culminating activity verbs will often have an extra argument that acts as an occurrence identifier. Let us consider, for example, a scenario involving an engineer, John, who worked on engine 2 repairing faults of the engine at several past times. John started to repair a fault of engine 2 on 1/6/1998 at 9:00 am (Figure 3.7). He continued to work on that fault up to 1:00 pm, at which point he temporarily abandoned the repair without completing it. He resumed the repair at 3:00 pm on 25/6/1998, and completed it at 5:00 pm on the same day. In 1999, John was asked to repair another fault of engine 2. He started the repair on 1/7/1999 at 9:00 am, and continued to work on that fault up to 1:00 pm on the same day without completing the repair. He then abandoned the repair for ever, because he was not qualified to fix that fault, and the repair was assigned to another engineer. Finally, in 2000 John was asked to repair a third fault of engine 2. He started to repair the fault on 1/6/2000 at 9:00 am, and continued to work on that fault up to 1:00 pm, without completing the repair. He resumed the repair at 3:00 pm, and completed it at 5:00 pm on the same day. Representing (3.155) as (3.156) is problematic. (Here j denotes John, and e2 denotes engine 2.) Let us assume that the question is submitted after 1/6/2000. One would expect the answer to be affirmative, since a complete past repair of engine 2 by John falls within 1/6/2000. In contrast, (3.156) causes the answer to be negative. The semantics of the Culm operator (Section 3.9) 1/6/1998
25/6/1998
1/7/1999
1/6/2000
p1
p2
p3
p4
9:00 am 1:00 pm repairing(o1,j,e2)
3:00 pm 5:00 pm repairing(o1,j,e2)
9:00 am 1:00 pm repairing(o2,j,e2)
9:00 am 1:00 pm repairing(o3,j,e2)
p5 3:00 am 5:00 pm repairing(o3,j,e2)
p6
p7
Culm[repairing(o1,j,e2)]
Culm[repairing(o3,j,e2)] p8 Culm[repairing(j,e2)]
Figure 3.7 Occurrence identifiers
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Chapter 3
requires et to start at the beginning of the earliest maximal period where repairing(j, e2) holds, i.e., at the beginning of p1 in Figure 3.7, and to end at the end-point of the latest maximal period where repairing(j, e2) holds, i.e., at the end of p5 in Figure 3.7. In other words, et must be p8 of Figure 3.7. The At operator requires et, i.e., p8 , to be also a subperiod of 1/6/2000. This is not the case, and the answer is negative. (3.155) Did John repair engine 2 on 1/6/2000? (3.156) At[1/6/2000, Past[ev , Culm[repairing(j, e2)]]]
The problem is that although John was repairing engine 2 during all five periods (p1 , p2 , p3 , p4 , p5 ), the five periods intuitively belong to different occurrences of the situation where John is repairing engine 2. The first two periods have to do with the repair of the first fault (occurrence 1), the third period has to do with the repair of the second fault (occurrence 2), and the last two periods relate to the repair of the third fault (occurrence 3). The Culm[repairing(j, e2)] of (3.156), however, does not distinguish between the three occurrences, and forces et to start at the beginning of p1 and end at the end-point of p5 . Instead, we would like Culm[repairing(j, e2)] to distinguish between the three occurrences: to require et to start at the beginning of p1 (beginning of the first repair) and to end at the end-point of p2 (completion of the first repair), or to require et to start at the beginning of p4 (beginning of the third repair) and to end at the end-point of p5 (completion of the third repair). Culm[repairing(j, e2)] should not allow et to be p3 , because the second repair does not reach its completion at the end-point of p3 . To achieve this, an occurrence-identifying argument is employed. Assuming that o1, o2, and o3 denote the three occurrences, repairing(o1, j, e2) is true only at ets that are subperiods of p1 or p2 , repairing(o2, j, e2) only at ets that are subperiods of p3 , and repairing(o3, j, e2) only at ets that are subperiods of p4 or p5 . In practice, the occurrence-identifying argument is always a variable. For example, (3.155) is now represented as (3.157) instead of (3.156). (3.157) At[1/6/2000, Past[ev , Culm[repairing(ov , j, e2)]]]
According to (3.157), the answer should be affirmative if there is an et and a particular occurrence ov of the situation where John is repairing engine 2, such that et starts at the beginning of the first period where ov is ongoing, et ends at the end-point of the last period where ov is ongoing, ov reaches its completion at the end-point of et, and et falls within the past and within 1/6/2000. Now, if (3.155) is submitted after 1/6/2000, the answer is affirmative.
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Occurrence identifiers are a step towards formalisms that treat occurrences of situations, sometimes called ‘events’, as objects in the modelled world (Parsons 1990; Kamp & Reyle 1993; Blackburn, Gardent, & de Rijke 1994; Hwang & Schubert 1994). In top all terms, i.e., all constants and variables, denote objects of the modelled world. Thus, allowing occurrence-identifying terms, like ov in (3.157), implies that occurrences of situations are also world objects. Unlike other formalisms, however, top does not treat these occurrence-identifying terms in any special way, and there is nothing in the definition of top to distinguish objects denoted by occurrence-identifiers from objects denoted by other terms.
. Tense anaphora and localisation time Although tense anaphora is not examined in any detail in this book (Section 2.12), it should be pointed out that top’s localisation time could be used to handle some cases of tense anaphora. In some cases, the anaphoric nature of tenses can be handled by storing the temporal window established by adverbials and verb forms of previous questions, and by requiring the situations of follow-up questions to fall within that window. top’s localisation time can capture this notion of previous window. Assuming, for example, that (3.158) is submitted after 1999, the At and Past operators of the corresponding formula (3.159) narrow lt to the period that covers exactly 1999. This period could be stored and used as the initial value of lt in (3.161), that expresses the follow-up question (3.160). In effect, (3.160) would be taken to mean (3.162). (3.158) (3.159) (3.160) (3.161) (3.162)
Was Mary the personnel manager in 1999? At[1999, Past[ev , manager of (mary, personnel)]] Who was the personnel manager? ?whv Past[ev , manager of (whv , personnel)] Who was the personnel manager in 1999?
This is only a rough sketch of the necessary mechanisms; improvements would be needed. For example, if (3.158) and (3.160) are followed by (3.163), which is represented as (3.164), lt must be reset to the whole time axis. (3.163) Who is (now) the personnel manager? (3.164) ?whv Pres[manager of (whv , personnel)]
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. Generic representatives of partitionings As noted in Section 3.7, habitual readings are taken to involve habitual homonyms of verbs, which introduce different predicates than the corresponding non-habitual homonyms. A remaining issue is how to represent habitual readings that involve times, as in (3.165). (3.165) cannot be represented as (3.166), because (3.166) says that at 5:00 pm on some day during the previous month BA737 had the habit of departing. In contrast, the reading that we wish to capture is that during the previous month BA737 had the habit of departing at 5:00 pm. (3.165) Last month BA737 (habitually) departed at 5:00 pm. (3.166) Part[monthc , monv , –1] ∧ Part[5:00pmg , fvv ] ∧ At[monv , At[fvv , Past[ev , hab depart(ba737)]]
To capture such habitual readings one would have to allow gappy partitioning names, like 5:00pmg , to appear as predicate arguments, or add universal quantification to top, to allow statements to be made about all the elements of a gappy partitioning. To avoid complicating the definition of top, we will instead assume that for each gappy partitioning, there is a pseudo-entity in the world that can be used as a generic representative of all the elements of the partitioning. (3.165) will, then, be represented as (3.167), where 5:00pm denotes the generic representative of the gappy partitioning 5:00pmg . Constants denoting generic representatives will be the same as the corresponding partitioning names, but without the ‘g ’ suffix. (3.167) Part[monthc , monv , –1] ∧ At[monv , Past[ev , hab depart time(ba737, 5:00pm)]]
. Summary top is a formal language, used to represent the meanings of the English questions that are submitted to the nlitdb. The denotation of a top formula with respect to st, the time point where the question is submitted, specifies what the answer to the corresponding English question should report. The denotations of formulae with respect to st are defined in terms of their denotations with respect to st, et, and lt. The event time et is a time period where the situation described by the formula holds, and lt, the localisation time, is a temporal window within which et must be placed.
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Temporal linguistic mechanisms are expressed in top using temporal operators that manipulate st, et, and lt. Several operators were defined. The Part operator picks a period from a partitioning of the time-axis. Pres and Past are used when expressing present and past verb forms. Perf is used in combination with Past to express the past perfect. Culm is used to represent non-progressive forms of culminating activity verbs. At, Before, and After are employed when expressing punctual and period adverbials, and when expressing subordinate clauses introduced by while, before, and after. Duration adverbials introduced by in and for are expressed using For. Fills can be used to represent durative readings, where the situation of the verb covers the whole localisation time. Begin and End are used to refer to time-points where situations start or stop. Finally, Ntense is employed to allow noun phrases to refer either to st or to the time of the verb’s tense. The next chapter shows how English questions can be mapped systematically to appropriate top formulae.
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Chapter 4
From English to TOP
“One step at a time.”
. Introduction This chapter shows how English questions submitted to an nlitdb can be mapped systematically to appropriate top formulae. The mapping is based on a slightly modified version of hpsg, which remains close to the theory of Pollard and Sag (1994). The hpsg version of this book contains additional mechanisms to handle temporal phenomena, and replaces Pollard and Sag’s semantic constructs by feature structures that represent top expressions. For the sake of brevity, hpsg mechanisms for phenomena not considered in this book will be ignored or presented in a simplified manner. Readers familiar with the main concepts of unification-based grammars (Shieber 1986) should be able to follow most of the discussion in this chapter. To grasp the full details, however, readers not acquainted with hpsg may wish to consult Pollard and Sag (1994) first. The hpsg version of this book was implemented as a grammar of the ale system (Carpenter 1992; Carpenter & Penn 2001); this will be discussed further in Chapter 6.
. HPSG basics In hpsg, each word and syntactic constituent is mapped to a sign, a feature structure of a particular form that provides information about the word or syntactic constituent. An hpsg grammar consists of signs for words, hereafter called lexical signs, as well as lexical rules, schemata, principles, and a sort hierarchy, all discussed below.
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Chapter 4
.. Lexical signs, lexical rules and sort hierarchy Lexical signs provide information about individual words. For example, the lexical sign of (4.1) provides information about the base form of to land in the airport domain (Section 2.4.5). (4.1)
phon synsem
land
head aux – verb aspect culmact cat spr np -prd 1 loc subj comps pp -prd, pform on 2 cat arg1 occr_var cont arg2 1 arg3 2
vform bse
landing_on
The ‘<’ and ‘>’ delimiters denote lists. Roughly speaking, the phon feature shows the sequence of words the sign corresponds to. (4.1) corresponds to the single word land. Apart from phon, every sign has a synsem feature, as well as other features that are not shown in (4.1). (Features not relevant to the discussion will often be omitted.) The value of synsem in (4.1) is itself a feature structure that has a feature loc. The value of loc is in turn a feature structure that has the features cat and cont; these correspond roughly to the syntactic category and the semantic content, respectively. Each hpsg feature structure belongs to a particular sort. The sort hierarchy of hpsg shows the available sorts, and the subsorts of each sort. It also specifies which features the members of each sort have, and the sorts the values of these features must belong to. In (4.1), for example, the value of head is a feature structure of sort verb; the sort name appears near the bottom left corner of the feature structure. The value of head signals that the word is the base form (vform bse) of a non-auxiliary (aux –) verb. The sort hierarchy of Pollard and Sag (1994) specifies that the value of head must be of sort head, and that verb is a subsort of head. This allows feature structures of sort verb to be used as values of head. The value of vform in (4.1) is an atomic feature structure, i.e., a feature structure with no features, of sort bse. For simplicity, when showing
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From English to TOP
feature structures, uninteresting sort names are ommitted; for example, (4.1) does not show the sort of loc’s value. aspect is the only new hpsg feature of this book. This feature will be present in feature structures of sort cat, which comprises all feature structures that can be used as values of the feature cat. The values of aspect are feature structures of sort aspect. The aspect sort, which is an addition of this book, contains only atomic feature structures, and has the subsorts: state, activity, culmact (culminating activity), and point. The state sort is in turn partitioned into: lex_state (lexical state), progressive (progressive state), and cnsq_state (consequent state). These sorts reflect the aspectual taxonomy of Chapter 2. Following Table 2.1 on page 29, (4.1) classifies the base form of to land as culminating activity. The spr, subj, and comps features of (4.1) provide information about the specifier, subject, and complements, respectively, that the verb has to combine with. Specifiers are determiners, like the, or words like much in much more and too in too late. Verbs do not admit specifiers, and hence the value of spr in (4.1) is the empty list. The subj value of (4.1) means that the verb requires a noun phrase as its subject. The np[-prd] 1 in (4.1) has the same meaning as in Pollard and Sag’s book (1994). Roughly speaking, it is an abbreviation for a sign that corresponds to a noun phrase. The -prd means that the noun phrase must be non-predicative; this will be discussed further in later sections. The 1 is intuitively a pointer to the world entity that the noun phrase denotes. Similarly, the comps value of (4.1) means that the verb requires as its complement a nonpredicative prepositional phrase introduced by on. The 2 is intuitively a pointer to the world entity of the prepositional phrase; for example, if the prepositional phrase is on a runway, the 2 is a pointer to the runway. The value of cont in (4.1) stands for the top predicate landing on(β, τ1 , τ2 ), where τ1 and τ2 are top terms corresponding to 1 and 2 , and β is a top variable acting as an occurrence identifier (Section 3.16).1 The exact relation between hpsg feature structures and top expressions will be discussed in later sections. To reduce the number of lexical signs that need to be provided manually, lexical rules can be used. These generate new lexical signs from existing ones. For example, lexical rules can be used to generate automatically the lexical signs of non-base verb forms from the corresponding base-form lexical signs. There will be several opportunities in this chapter to introduce and discuss lexical rules.
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.. Schemata and principles hpsg schemata specify basic combination patterns that are used when words or syntactic constituents combine to form larger constituents. For example, the head-complement schema is the pattern that is used, among other cases, when a verb combines with its complements. This is the schema that is used when landed combines with a complement like on runway 2; the verb is said to be the head daughter of the constituent landed on runway 2. The head-subject schema is used, among other cases, when a verb phrase combines with its subject. It is used, for example, when landed on runway 2 combines with its subject BA737; in this case, the verb phrase is the head daughter of BA737 landed on runway 2. No modifications to the schemata of Pollard and Sag (1994) will be introduced in the hpsg version of this book, and hence schemata will not be discussed further. hpsg principles control the propagation of feature values from the signs of words or syntactic constituents to the signs of their super-constituents. The head-feature principle, for example, specifies that the sign of the superconstituent inherits the head value of the head daughter’s sign. This causes the sign of landed on runway 2 to inherit the head value of the sign of landed, and the same value to be inherited by the sign of BA737 landed on runway 2. This book uses simplified versions of Pollard and Sag’s semantics principle and constituent ordering principle, and introduces one new principle, the aspect principle; all three principles will be discussed in later sections. All other principles follow Pollard and Sag (1994).
. Representing TOP yes/no formulae in HPSG According to Pollard and Sag (1994), the cont value of (4.1) would actually be (4.2).
(4.2)
quants
nucleus psoa
landing_on
arg1 occr_var arg2 1 2 arg3
The sort name ‘psoa’ stands for ‘parameterised state of affairs’, a term from situation theory (Cooper, Mukai, & Perry 1990). The semantic analysis of this book is not situation-theoretic, but the term ‘psoa’ is still used for compatibility
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From English to TOP
psoa predicate arg1
circling
ind
arg1 arg2 arg3
landing_on
operator occr_var ind ind
...
main_psoa
pres
psoa
...
Figure 4.1 Subsorts of psoa in this book
with Pollard and Sag. In Pollard and Sag’s treatment, feature structures of sort psoa have two features: quants and nucleus. The quants feature, which is part of hpsg’s quantifier scoping mechanisms, is not used in this book. This leaves only one feature, nucleus, in psoas. For simplicity, nucleus will also be ignored, and the psoa sort will be taken to contain the feature structures that would be values of nucleus in Pollard and Sag’s treatment. More precisely, in this book psoa has two subsorts: predicate and operator (Figure 4.1). Feature structures of sort psoa are used to represent top yes/no formulae. The predicate sort contains feature structures that represent top predicates, while operator contains feature structures that represent all other yes/no formulae. The predicate sort has domain-specific subsorts, corresponding to domain-specific predicate functors. In the airport domain, for example, landing_on is a subsort of predicate. The feature structures in the subsorts of predicate carry features named arg1, arg2, arg3, etc., which represent the arguments of the predicates. The values of arg1, arg2, etc. are of sort ind. In (4.1) and (4.2), occr_var is a subsort of ind that is used to represent occurrence identifiers (Section 3.16). The ind sort and its subsorts will be discussed further below. The operator sort has the subsorts shown in Figure 4.2, which correspond to the top operators of Chapter 3. There is no subsort for Fills, as this operator is ignored in the remainder of this book. There is also no subsort for the Part[σ, β, νord ] version of the Part operator; to save space, this operator is not used in the rest of this book, and the periods of words like yesterday are represented using top constants, rather than expressions of the form Part[dayc , β, –1]. An additional subsort, and, is present in Figure 4.2; this stands for top’s conjunction. The order of the features in Figure 4.2 corresponds to the order of the arguments of the top operators. For example, the
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Chapter 4 main_psoa pres et_handle main_psoa past et_handle main_psoa perf time_spec main_psoa at_op time_spec main_psoa
before_op
psoa
tvar + temp_ent psoa tvar + temp_ent psoa temp_ent ∨ psoa psoa temp_ent ∨ psoa psoa
main_psoa predicate culm conj1 psoa conj2 psoa and
begin
end
main_psoa
psoa
main_psoa
psoa
dur_unit
duration main_psoa
for_op time_spec temp_ent ∨ psoa main_psoa psoa after_op tvar + et_handle now ∨ temp_ent main_psoa psoa ntense tvar – partng compl_partng ∨ gappy_partng tvar + part_var
part
compl_partng tvar – sem_num psoa
temp_ent
Figure 4.2 Subsorts of operator
et_handle and main_psoa features of the past sort correspond to the first and second arguments of top’s Past[β, φ], respectively. In Pollard and Sag’s theory (1994), feature structures of sort ind, called indices, have the features person, number, and gender, which are used to enforce person, number, and gender agreement, respectively. For simplicity, these features are ignored in the hpsg version of this book, and no agreement checks are made. Pollard and Sag’s subsorts of ind (ref, there, it), which are used in hpsg’s binding theory, are also ignored. In this book, indices stand for top terms, i.e, constants or variables. The situation is roughly speaking as in Figure 4.3. For each top constant, for example, ba737 or gate2, there is a subsort of ind that represents that constant. There is also a subsort var of ind, whose indices represent top variables. A tvar feature is used to distinguish indices that represent constants from indices that represent variables. All indices of
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From English to TOP
ind tvar
ba737
–
tvar
uk160
–
tvar
gate2
– ...
tvar +
var
Figure 4.3 Subsorts of ind in this book – simplified version
constant-representing sorts have their tvar set to –. Indices of var have their tvar set to +. The fact that there is only one subsort for top variables in Figure 4.3, var, does not mean that only one top variable can be represented: var is a sort of feature structures, containing infinitely many feature-structure members. Unless unified, any two of these members are taken to represent different top variables. Each subsort of ind that represents a top constant also contains infinitely many different feature-structure members. In this case, however, all members of the subsort are taken to represent the same constant. For example, any feature structure of sort gate2 represents the top constant gate2.
. More on the subsorts of ind The subsorts of ind are actually more complicated than in Figure 4.3. As discussed in Section 1.2, natural language interfaces often employ a domaindependent hierarchy of entity types, as part of their ontology. Here, a hierarchy of this kind is mounted under the ind sort (Androutsopoulos & Dale 2000), as explained below. In the airport domain, there are temporal entities, like the year 2000, the Monday 27/8/2001, etc., and non-temporal entities, such as flight BA737 and gate 2. Indices representing temporal entities are classified into a subsort of ind called temp_ent, while indices representing non-temporal entities are classified into non_temp_ent; see Figure 4.4, ignoring partng and its subsorts for the moment. The non_temp_ent sort has in turn subsorts like mass, which comprises indices representing mass entities, such as foam or water, and flight_ent, which includes indices representing flights. The flight_ent sort has one subsort for each top constant that denotes a flight (e.g., ba737, uk160), plus one sort, called flight_ent_var, whose indices represent top variables that denote flights; this is similar to the var sort in the simplified version of Figure 4.3. The other subsorts of non_temp_ent are organised in a similar manner.
minute_gappy day_gappy
gappy_partng
day_ent
Figure 4.4 The sorts partng and ind with their subsorts
5:00pm1/1/91 9:00am1/5/92 ... minute_ent_var 1/1/91 1/5/92 ... day_ent_var
minute_ent
mass
...
Jan91 Jun93 ... month_ent_var
month_ent
gate1 gate2
flight_ent
occr_var
...
ba737 uk160 ... flight_ent_var
other_temp_ent_var
... gate_ent_var
gate_ent
non_temp_ent
... foam water ... mass_ent_var
monday tuesday ... day_gappy_var 5:00pm 9:00am ... minute_gappy_var temp_ent
minute day month ...
compl_partng
ind
partng
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From English to TOP
The temp_ent sort has subsorts like minute_ent, which comprises indices representing particular minutes, such as the 5:00 pm minute of 1/1/2001, day_ent, which comprises indices representing particular days, etc. The minute_ ent sort has one subsort for each top constant that denotes a particular minute, plus the sort minute_ent_var, whose indices represent top variables that denote particular minutes; this is again similar to the var sort of Figure 4.3. The other subsorts of temp_ent are similar. As in Section 4.3, indices of sorts that represent top constants have their tvar set to –, while indices of sorts that represent top variables have their tvar set to +. The occr_var sort of Figure 4.4 contains indices that represent top variables used as occurrence identifiers (Section 3.16). There is also a special sort now, not shown in Figure 4.4, which is used to represent the top expression now* (Section 3.13). Going back to Figure 4.2, it should now be easy to see that its sorts mirror the definitions of top’s operators. For example, the ntense sort reflects the fact that the first argument of an Ntense operator must be now* or a variable (tvar +) denoting a period (temp_ent), while the second argument must be a yes/no formula (psoa). The sem_num sort in for_op is a child of non_temp_ent, not shown in Figure 4.4, with subsorts that represent the numbers 1, 2, 3, etc. Let us now examine the partng sort of Figure 4.4 and its subsorts compl_partng and gappy_partng, which do not exist in Pollard and Sag’s (1994) treatment. For each top complete or gappy partitioning name, such as minutec , dayc , 5:00pmg , or mondayg , there is a leaf-subsort of compl_partng or gappy_partng, respectively, which represents that name. In Figure 4.4, the sorts 5:00pm, 9:00am, etc. are grouped under minute_gappy to reflect the fact that the corresponding partitionings contain minute-periods. Similarly, monday, tuesday, etc. are grouped under day_gappy as the partitionings contain dayperiods. Section 4.12 below provides examples where sorts like minute_gappy and day_gappy prove useful. Apart from gappy partitioning names, the subsorts of gappy_partng are also used to represent top terms that denote generic representatives of gappy partitionings (Section 3.18). This is why gappy_partng is a subsort of both partng and ind in Figure 4.4. For example, (4.4), which expresses the habitual reading of (4.3), is represented as (4.5). In this case, the subsort 5:00pm of gappy_partng represents the top constant 5:00pm, which in turn denotes the generic representative of the gappy partitioning 5:00pmg . (4.3) BA737 departs (habitually) at 5:00 pm (4.4) Pres[hab departs at(ba737, 5:00pm)]
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Chapter 4
(4.5)
main_psoa
arg1 arg2 hab_departs_at
pres
tvar – ba737 tvar – 5:00pm
In contrast, (4.7), which expresses the non-habitual reading of (4.6), is represented as (4.8). In this case, the subsort 5:00pm of gappy_partng stands for top’s partitioning name 5:00pmg . (It cannot represent a top term, because top terms cannot be used as first arguments of Part operators.) The two 1 s in (4.8) force the values of part_var and time_spec to be unified, i.e., they must represent the same top variable. (4.6) BA737 departed (actually) at 5:00 pm. (4.7) Part[5:00pmg , fvv ] ∧ At[fvv , Past[ev , depart(ba737)]] (4.8) tvar – partng conj1 part_var part time_spec conj2 main_psoa
and
at_op
5:00pm
past
tvar + temp_ent
arg1 tvar – ba737
tvar + 1
temp_ent 1
et_handle main_psoa
depart
Sorts like minute_gappy_var and day_gappy_var in Figure 4.4 are used to represent top variables that denote generic representatives of gappy partitionings. The indices of these sorts have their tvar set to +, while the indices of all other leaf-subsorts of gappy_partng have their tvar set to –. The hierarchy under ind is domain-dependent. For example, in an application where the database contains information about a company, the subsorts of non_temp_ent would correspond to departments, managers, etc. It is assumed, however, that in all application domains, ind would have at least the immediate subsorts temp_ent, non_temp_ent, occr_var, and gappy_partng. It is also assumed that the subsorts of partng and temp_ent would have the general form of Figure 4.4, though they would have to be adjusted to reflect the partitionings and temporal entities used in the particular application.
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From English to TOP
. Representing TOP quantifiers in HPSG We have so far examined how top yes/no formulae are represented in the hpsg version of this book using feature-structures of sort psoa (Figure 4.1). To represent top wh-formulae, i.e., formulae with interrogative or interrogativemaximal quantifiers, additional feature-structure sorts are needed, as discussed below. In hpsg (Pollard & Sag 1994), feature structures of sort quant represent unresolved quantifiers, i.e., quantifiers whose scope is not known. They have two features: det and restind (restricted index), as shown in (4.9). The det feature shows the type of the quantifier; in this book, det can have the values exists (existential quantifier), interrog (interrogative quantifier), and interrog_mxl (interrogative-maximal quantifier).
exists ∨ interrog ∨ interrog_mxl index tvar + restind ind restr set(psoa)
(4.9)
det
nom_obj
quant
The values of restind are feature structures of sort nom_obj (nominal object).2 These have the features index, whose values are of sort ind, and restr, whose values are sets of psoas. When a nom_obj feature structure is the value of restind, the index corresponds to the top variable being quantified, and the restr corresponds to the range of the quantifier. If the restr set contains more than one psoas, the psoa-elements of the set are treated as forming a conjunction. For example, (4.10) represents (4.11).
interrog index tvar + 1 ind restind arg1 1 restr
(4.10)
quant
det
nom_obj
flight
(4.11) ?f v flight(f v )
Although top does not use explicit existential quantifiers, the hpsg version of this book represents existential quantifiers explicitly, using quants whose det is exists, for compatibility with Pollard and Sag (1994). As will be explained in Section 4.6 below, these explicit existential quantifiers are removed when extracting top formulae from hpsg signs.
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. Extracting TOP formulae from HPSG signs During the parsing, each question is mapped to one or more signs, with each sign corresponding to a possible reading of the question. An example of a resulting sign is shown in (4.12). We ignore in this section Ntense operators, which will be discussed further in Section 4.9. It is also assumed that multitoken names, like gate 2, have been concatenated during the preprocessing stage; we will return to this point in later sections. phon which, inspector, was, at, gate2 vform fin head aux + verb aspect lex_state cat spr subj synsem | loc comps et_handle tvar + (4.12) temp_ent cont 1 arg1 main_psoa arg2 gate2 located_at past det interrog 1 tvar + index person_ent qstore restind 1 arg1 restr inspector nom_obj quant
Apart from the features that were discussed in Section 4.2, signs also have the feature qstore (quantifier store), whose values are sets of quants (Section 4.5). In the hpsg version of this book, the cont value of signs that correspond to questions is of sort psoa, i.e., it represents a top yes/no formula. The qstore value represents quantifiers that must be inserted in front of the formula of cont. In the prototype nlitdb that will be presented in Chapter 6, there is an extractor of top formulae that examines the cont and qstore features of the question’s sign, and generates the corresponding top formula. The extractor first examines recursively the features of cont, rewriting them in term notation; in (4.12), this generates (4.13). For each element of qstore, the extractor
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From English to TOP
then adds a suitable quantifier in front of the formula of cont; in (4.12), this transforms (4.13) into (4.14). (4.13) Past[ev , located at(pv , gate2)] (4.14) ?pv inspector(pv ) ∧ Past[ev , located at(pv , gate2)]
Since free top variables are implicitly existentially quantified, with elements of qstore that correspond to existential quantifiers, no explicit existential quantifier is added to the formula of cont; only the expression that corresponds to the restr of the quant-element is added. For example, if the det of (4.12) were exists, (4.14) would be (4.15). (4.15) inspector(pv ) ∧ Past[ev , located at(pv , gate2)]
. Verb forms Let us now examine in more detail how the various linguistic constructs are treated in the hpsg grammar of this book, focusing on the temporal mechanisms of Chapter 2; these are not addressed by Pollar and Sag (1994). .. Single-word verb forms Single-word non-base verb forms are generated automatically from the signs of the corresponding base forms using lexical rules. The signs for simple present forms are generated by (4.16). (4.16) Simple Present Lexical Rule:
phon λ synsem | loc
cat cont
vform bse head aux – verb aspect lex_state 1
⇓
phon morph(λ, simple_present) vform fin head aux – cat verb synsem | loc aspect lex_state main_psoa 1 cont pres
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For each lexical sign that matches the first feature structure, the left-hand side of the rule, a new lexical sign is generated as shown in the second feature structure, the right hand side of the rule. Following standard hpsg notation, synsem|loc refers to the loc feature of the value of synsem. The head value of the left-hand side requires the original sign to correspond to the base form of a non-auxiliary verb; auxiliary verbs are treated separately. The head value of the right-hand side signals that the resulting sign corresponds to a finite verb form, i.e., a form that does not need to combine with an auxiliary verb. The cont of the new sign is the same as the cont of the original one, except that it contains an additional Pres operator. Features of the original sign not shown in the left-hand side, for example subj and comps, have the same values in the generated sign. The original sign is required to correspond to a lexical state base form. No simple present signs are generated for verbs whose base forms are not states, in accordance with the assumption of Section 2.5.1 that the simple present can be used only with state verbs. The notation morph(λ, simple present) in the rule denotes a morphological transformation that generates the simple present form (e.g., contains) from the base form (e.g., contain). The prototype nlitdb of Chapter 6 actually employs two different simple present lexical rules. These generate signs for singular and plural simple present forms, respectively. As mentioned in Sections 2.13 and 4.3, plurals are treated semantically as singulars, and no number agreement checks are made. Hence, the two lexical rules differ only in the phon values of the generated signs. (4.17) shows the base form sign of to contain in the airport domain. From (4.17), (4.16) generates (4.18). The tank_ent and mass_ent in (4.17) and (4.18) require the indices introduced by the subject and object to be of sort tank_ent and mass_ent, respectively; tank_ent is a sister of flight_ent in Figure 4.4. Hence, the semantically anomalous gate 2 contains water, where the subject introduces an index of sort gate2, which is not a subsort of tank_ent, would be rejected. All lexical signs of verb forms have their qstore set to {}. To save space, the qstore features are not shown here.
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From English to TOP
(4.17)
phon contain cat synsem | loc cont
head aux – verb aspect lex_state spr subj np -prd tank ent 1 comps np -prd mass ent 2 arg1 1 arg2 2
vform bse
contains
(4.18) phon contains cat synsem | loc cont
head aux – verb aspect lex_state spr subj np -prd tank ent 1 comps np -prd mass ent 2 arg1 1 main_psoa arg2 2
vform fin
contains
pres
The simple past signs of culminating activity verbs are generated by the lexical rule of (4.19). The simple past signs of non-culminating activity verbs are generated by a lexical rule that is similar to (4.19), except that it does not introduce a Culm operator in the resulting sign. (4.19) Simple Past Lexical Rule (Culm. Activity Base Form):
phon
λ
synsem | loc
head cat aspect cont 1
⇓
vform bse aux – verb culmact
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Chapter 4 phon morph(λ, simple_past) vform fin head aux – cat verb aspect culmact synsem | loc et_handle tvar + temp_ent cont main_psoa main_psoa
1
culm
past
The signs of past participles (e.g., inspected in ‘Who had inspected BA737?’) are generated by two lexical rules that are similar to the simple past ones. There is a rule for culminating activity verbs, which introduces a Culm operator in the past participle sign, and a rule for non-culminating activity verbs, which does not introduce a Culm operator. The generated signs have their vform set to psp (past participle), and the same aspect as the base signs, i.e., their aspect is not changed to cnsq_state (consequent state). The shift to consequent state takes place when the auxiliary had combines with the past participle; this will be discussed in Section 4.7.2. The signs for present participles (e.g., servicing in ‘Which company is servicing BA737?’) are generated by (4.20). The present participle signs are the same as the base ones, except that their vform is prp (present participle), and their aspect is progressive (progressive state). In English, there is no morphological distinction between gerunds and present participles. hpsg and most traditional grammars, however, distinguish between the two (Thomson & Martinet 1986). In (4.21), the inspecting is the gerund of to inspect, while in (4.22), it is the present participle. Gerund signs are generated by a lexical rule that is similar to (4.20), except that the generated signs retain the aspect of the original ones, and have their vform set to ger. (4.20) Present Participle Lexical Rule:
phon
λ
synsem | loc
head cat aspect cont 1
⇓
vform bse aux – verb aspect
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From English to TOP
morph(λ, present_participle) vform prp head aux – cat verb synsem | loc aspect progressive 1 cont phon
(4.21) J. Adams finished inspecting BA737. (4.22) J. Adams was inspecting BA737.
The fact that gerund signs retain the aspect of the base signs is used in the treatment of verbs like to finish (Section 2.6). The simple past finished receives multiple signs, which are generated from corresponding base form signs by the simple past lexical rules. (4.23) is used when finished combines with a culminating activity verb phrase, and (4.24) when it combines with a state or activity verb phrase (‘ss|l’ is an abbreviation of ‘synsem|loc’). (4.23)
phon ss | l
finished vform fin head aux – verb aspect point cat spr 1 subj 1 , vform ger, subj comps vp 2 : aspect culmact tvar + et_handle temp_ent
cont main_psoa main_psoa main_psoa past
end
culm
2
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Chapter 4
(4.24)
phon ss | l
finished vform fin head aux – verb aspect point cat spr 1 subj comps vp subj 1 , vform ger, : 2 aspect state ∨ activity et_handle tvar + temp_ent cont main_psoa main_psoa 2 past
end
In (4.23), the comps value means that finished requires as its complement a gerund verb phrase, i.e., a gerund that has combined with its complements but not its subject, whose aspect must be culminating activity. The 1 of comps points to a description of the required subject of the gerund verb phrase, and the 2 is a pointer to the cont value of the sign of the gerund verb phrase. The two 1 s in (4.23) have the effect that finished requires as its subject whatever the gerund verb phrase requires as its subject. The two 2 s cause the sign of finished to inherit the cont value of the sign of the gerund verb phrase, but with additional Past, End, and Culm operators. (4.24) is similar, but it introduces no Culm operator. In (4.21), the sign of the gerund inspecting retains the aspect of the base sign, which in the airport domain is culmact. The sign of the gerund verb phrase inspecting BA737 inherits the culmact aspect of the gerund sign; this follows from the aspect principle, which will be discussed in Section 4.11.1. Hence, (4.23) is used, causing (4.21) to receive a sign whose cont represents (4.25), i.e., the inspection must have been completed. (4.25) Past[ev , End[Culm[inspecting(occrv , ja, ba737)]]]
In contrast, in (4.26) the sign of circling inherits the activity aspect of the base sign, causing (4.24) to be used. This leads to (4.27), which does not require any completion point to have been reached. (4.26) BA737 finished circling. (4.27) Past[ev , End[circling(ba737)]]
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From English to TOP
There is also a sign of the simple past finished for the case where the gerund verb phrase is a point. In that case, the cont of the sign of finished is identical to the the cont of the sign of the gerund verb phrase, i.e., finished has no semantic contribution, in accordance with Section 2.6. The signs of started, stopped, and began are similar, except that they introduce Begin operators instead of End ones. Unlike finished, the signs of stopped do not introduce Culm operators when stopped combines with culminating activities, reflecting the fact that there is no need for a completion point to have been reached. .. Auxiliary verbs and multi-word verb forms We now move on to auxiliary verbs and multi-word verb forms, such as had departed and is inspecting. The sign of the simple past auxiliary had is shown in (4.28). The sign requires a past participle verb phrase to be used as a complement of had. The effect of the 1 s is that had requires as its subject whatever the past participle verb phrase requires as its subject. The 2 s cause the main_psoa value of the perf to be the same as the cont value of the sign of the past participle verb phrase. (4.28)
phon ss | l
had
head aux + verb aspect cnsq_state cat spr 1 subj 1 , vform psp : 2 comps vp subj tvar + et_handle temp_ent cont et_handle tvar + temp_ent main_psoa main_psoa 2
past
vform fin
perf
In the airport domain, the past participle departed receives multiple signs, corresponding to various habitual and non-habitual uses of the verb; these are generated from the corresponding base form signs by the lexical rules of Section 4.7.1. In (4.29), the sign of (4.30) is used. According to (4.30), departed requires no complements, i.e., it counts as a verb phrase and can be used as the
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complement of had. When had combines with departed, the subj of (4.28) becomes the same as the subj of (4.30), and the main_psoa of the perf in (4.28) becomes the same as the cont of (4.30), because of the 1 s and 2 s in (4.28), respectively. The resulting constituent had departed receives (4.31). (4.29) BA737 had departed. (4.30) phon departed ss | l
head aux – verb aspect point cat spr subj np -prd flight ent 3 comps arg1 3 cont
vform psp
actl_depart
(4.31)
phon ss | l
had, departed
vform fin head aux + verb aspect cnsq_state cat spr subj np -prd flight ent 3 comps tvar + et_handle temp_ent et_handle tvar + cont temp_ent main_psoa main_psoa arg1 3 actl_depart
past
perf
The hpsg principles, including the semantics and aspect principles that will be discussed in later sections, cause (4.31) to inherit the head, aspect, spr, subj, and cont values of (4.28). Consequently, the aspect of had departed becomes consequent state, whereas departed was a point; this is in accordance with the aspectual shift of Section 2.5.5. As will be explained further in Section 4.9, the proper name BA737 contributes an index that represents the flight BA737. When had departed com-
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From English to TOP
bines with its subject BA737, the index of BA737 becomes the arg1 value of (4.31), because of the 3 s of (4.31). This causes (4.29) to receive a sign whose cont corresponds to (4.32). (4.32) Past[e1v , Perf [e2v , actl depart(ba737)]]
As discussed in Sections 2.5.4 and 3.15, present perfect forms are treated semantically as simple past forms. This is why the sign of has, shown in (4.33), does not introduce a Perf operator, and preserves the aspect of the past participle, unlike the sign of had. This causes BA737 has departed to receive the same top formula as BA737 departed. (4.33)
phon ss | l
has
head aux + verb aspect 1 cat spr subj 2 comps vp subj 2 , vform psp, aspect 1 : 3 tvar + et_handle temp_ent cont main_psoa 3
vform fin
past
The auxiliary does is given the sign of (4.34), which indicates that a base verb phrase is required as a complement. In accordance with the assumption of Section 2.5.1 that the simple present can be used only with state verbs, the verb phrase complement of does is required to be a lexical state. (4.34) and the habitual base sign of (4.35) cause (4.36) to receive (4.37); in this case, Airserve is the subject of both does and service.
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Chapter 4
(4.34)
phon ss | l
does
head aux + verb aspect lex_state 1 cat spr 2 subj comps vp subj 2 , vform bse, aspect 1 : 3 main_psoa 3 cont
vform fin
pres
(4.35) phon ss | l
service
head aux – verb aspect lex_state cat spr subj np -prd company ent 4 comps np -prd flight ent 5 4 arg1 cont arg2 5 vform bse
hab_servicer_of
(4.36) Does Airserve service BA737? (4.37)
phon ss | l
does, Airserve, service, BA737 vform bse head aux + verb aspect lex_state cat spr subj comps arg1 cont main_psoa arg2 pres
hab_servicer_of
airserve ba737
In the airport domain, there is an additional sign for the base form of to service, which corresponds to the non-habitual homonym. This is similar to (4.35), but
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From English to TOP
it introduces the predicate functor actl servicing and its aspect is culmact. This sign cannot be used in (4.36), because (4.34) requires the verb phrase complement to be a state, not a culminating activity. This correctly predicts that (4.36) cannot be asking if Airserve is actually servicing BA737 at the present moment. The auxiliary did receives two signs. The first one, shown in (4.38), is for culminating activity verb phrase complements. The second one is used with state, activity, and point verb phrase complements; it is similar to (4.38), but does not introduce a Culm. In both cases, a Past is added. (4.38)
phon ss | l
did
vform fin head aux + verb aspect culmact 1 cat spr 2 subj comps vp subj 2 , vform bse, aspect 1 : 3 tvar + et_handle temp_ent cont main_psoa main_psoa 3
past
culm
The non-habitual sign of service and (4.38) cause (4.39) to be mapped to (4.40), which requires Airserve to have actually serviced BA737 in the past. The habitual sign of (4.35) and the did sign for non-culminating activity complements cause (4.39) to be mapped to (4.41), which requires Airserve to have been a past habitual servicer of BA737. (4.39) Did Airserve service BA737? (4.40) Past[ev , Culm[actl servicing(occrv , airserve, ba737)]] (4.41) Past[ev , hab servicer of (airserve, ba737)]
The sign for the is auxiliary is shown in (4.42). Its functionality can be illustrated by considering the present participle servicing, which receives two signs in the airport domain: a non-habitual one, shown in (4.43), and a habitual one. The latter is similar to (4.43), but it introduces the functor hab servicer of , and its aspect is lex_state.
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(4.42)
phon ss | l
is
head aux + verb aspect progressive cat spr 1 subj comps vp subj 1 , vform prp : 2 main_psoa 2 cont
vform fin
pres
(4.43) phon ss | l
servicing vform prp head aux – verb aspect culmact cat spr subj np -prd company ent 1 comps np -prd flight ent 2 arg1 occr_var cont arg2 1 arg3 2 actl_servicing
(4.42) and (4.43) cause (4.44) to be mapped to (4.45), which requires Airserve to be actually servicing BA737 at the present. In contrast, (4.42) and the habitual present participle sign of servicing cause (4.44) to be mapped to (4.46), which requires Airserve to be the current habitual servicer of BA737. The latter reading follows from the arrangements of Section 2.5.3, which allow state verbs to be used in progressive forms with the same meanings as the corresponding non-progressive forms. (4.44) Airserve is servicing BA737. (4.45) Pres[actl servicing(occrv , airserve, ba737)] (4.46) Pres[hab servicer of (airserve, ba737)]
The sign for the auxiliary was is similar to (4.42), except that it introduces a Past operator instead of a Pres one.
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From English to TOP
. Predicative and non-predicative prepositions Following Pollard and Sag (1987:65), prepositions receive separate signs for their predicative and non-predicative uses. In sentences like (4.47) and (4.48), where the prepositions introduce complements of to be, the prepositions are said to be predicative. In (4.49) and (4.50), where they introduce complements of other verbs, the prepositions are non-predicative. (4.47) (4.48) (4.49) (4.50)
BA737 is at gate 2. BA737 was on runway 3. BA737 (habitually) arrives at gate 2. BA737 landed on runway 3.
Predicative prepositions introduce their own top predicates, while nonpredicative prepositions have no semantic contribution; this is discussed further in the following paragraphs. .. Predicative prepositions The predicative sign of at is shown in (4.51); the predicative signs of other prepositions are similar. The ‘prd +’ shows that the sign is predicative. The pform feature reflects the preposition the sign corresponds to. Signs for prepositional phrases inherit the pform of the preposition’s sign, which is useful with verbs that require prepositional phrases introduced by particular prepositions. (4.51)
phon ss | l
at
cat cont
head prd + prep spr subj np -prd 1 comps np -prd 2 arg1 1
located_at
pform at
arg2 non_temp_ent
2
The prd feature is also used to distinguish predicative from non-predicative uses of adjectives and nouns; this will be discussed in Sections 4.9 and 4.10. According to (4.51), at requires a non-predicative noun phrase as its subject, and another one as its complement; in (4.47), the noun phrases are BA737 and
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gate 2, respectively. The 1 and 2 of (4.51) correspond to the indices that denote the entities of BA737 and gate 2, respectively. (4.52) shows the resulting sign for the prepositional phrase at gate 2. (4.52)
phon ss | l
at, gate2 cat cont
head prd + prep spr subj np -prd 1 comps arg1 1 arg2 gate2
pform at
located_at
Apart from (4.42), which is used when is combines with a present-participle complement, the is auxiliary is also given the lexical sign of (4.53), which is used when is combines with predicative prepositional phrases. (4.53)
phon ss | l
is
head aux + verb aspect lex_state cat spr 3 subj comps pp subj 3 , prd + : 4 main_psoa 4 cont
vform fin
pres
According to (4.53), is requires as its complement a predicative prepositional phrase, i.e., a predicative preposition that has combined with its complements but not its subject, like the at gate 2 of (4.52). (4.52) and (4.53) cause (4.47) to receive (4.54).
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From English to TOP
(4.54)
phon ss | l
BA737, is, at, gate2 vform fin head aux + verb cat aspect lex_state spr subj comps arg1 cont main_psoa arg2 located_at
pres
ba737 gate2
Like is, the was auxiliary receives two signs: one for present participle complements, as in BA737 was circling, and one for predicative prepositional phrase complements, as in (4.48). These are similar to the signs of is, but they introduce Past operators rather than Pres ones. .. Non-predicative prepositions The non-predicative sign of at is shown in (4.55); the non-predicative signs of other prepositions are similar. The effect of the 1 s is that the cont value of the sign of at is the same as the cont value of the sign of the noun phrase complement of at; i.e., the at has no additional semantic contribution. (4.55)
phon ss | l
at
cat cont
head prd – prep spr subj comps np -prd : 1
pform at
1
(4.55) and the habitual sign of arrives of (4.56) cause (4.49) to receive (4.57).
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(4.56)
phon ss | l
arrives
head aux – verb aspect lex_state cat spr subj np -prd flight ent 1 comps pp -prd, pform at gate ent 2 arg1 1 cont main_psoa arg2 2 pres
(4.57)
phon ss | l
vform fin
hab_arrive_at
BA737, arrives, at, gate2 vform fin head aux – verb aspect lex_state cat spr subj comps arg1 cont main_psoa arg2 pres
hab_arrive_at
ba737 gate2
The predicative and non-predicative prepositional signs of this section are not used when prepositions introduce temporal adverbials, as in BA737 departed (actually) at 5:00 pm. There are additional prepositional signs for these cases, which will be discussed in Section 4.11.
. Nouns Like prepositions, nouns receive different signs for their predicative and nonpredicative uses. Nouns used as heads (main nouns) in noun phrase complements of to be, like the president in (4.58), are predicative. The noun phrase complements are also said to be predicative. In all other cases, like the president in (4.59), the nouns and noun phrases are non-predicative.
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From English to TOP
(4.58) J. Adams is the president. (4.59) The president was at gate 2.
.. Non-predicative nouns Let us first examine non-predicative nouns. (4.60) shows the sign of president that would be used in (4.59). The prd value signals that the sign corresponds to a non-predicative use of the noun. The spr value declares that the noun requires as its specifier a determiner (e.g., a, the). phon president prd – head noun cat spr loc | cat | head det subj comps (4.60) ss | l index person_ent 1 et_handle tvar + ∨ now cont temp_ent restr 1 main_psoa arg1 president ntense nom_obj qstore {}
The cont values of signs that correspond to non-predicative nouns are of sort nom_obj (Section 4.5). The index value stands for the world entity described by the noun, and the restr value represents top expressions that are introduced by the noun. For simplicity, the determiner the will be treated as equivalent to the determiner a. The sign of the that is used in (4.59) is shown in (4.61), where ‘spec|l’ is an abbreviation of ‘spec|loc’.
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Chapter 4 phon the head spec | l cat det (4.61) ss | l spr subj comps det exists
cont restind index quant 3 qstore
prd – head noun spr _ cat subj comps cont 2 3 tvar + 2
The spec feature of (4.61) declares that the must be used as the specifier of ¯ i.e., as the specifier of a non-predicative noun that has a non-predicative N, combined with its complements and requires a specifier (spr < >). The 3 s of (4.61) cause an existential quantifier to be inserted into the quantifier store (Section 4.6), and the 2 s cause the restind of that quantifier to be unified with ¯ sign. the cont of the N’s According to (4.60), president is non-predicative, it does not need to combine with any complements, and requires a specifier. Hence, it satisfies the spec restrictions of (4.61), and the can be used as the specifier of president. When the combines with president, the restind of (4.61) is unified with the cont of (4.60), and the qstore of (4.61) becomes a set containing (4.62). The resulting noun phrase receives (4.63), where 2 and 3 are as in (4.62).
exists index (4.62) restind restr quant
det
nom_obj
tvar
+ 1
person_ent 3 et_handle tvar + ∨ now 2 temp_ent main_psoa arg1 1 president ntense
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From English to TOP phon the, president prd – head noun spr cat subj (4.63) ss | l comps 2 cont 3 qstore
By the head feature principle (Section 4.2.2), (4.63) inherits the head of (4.60), which is the sign of the head daughter in this case. The propagation of cont and qstore is controlled by the semantics principle, which in this book has the simplified form of (4.64). (4.64) uses the terminology of Pollard and Sag (1994); it is explained further directly below. (4.64) Semantics Principle (simplified version of this book): In a headed phrase, (a) the qstore value is the union of the qstore values of the daughters, and (b) the synsem|loc|cont value is token-identical with that of the semantic head. (In a headed phrase, the semantic head is the adjunct-daughter if any, and the head-daughter otherwise.)
Part (a) of the semantics principle means that the qstore of each syntactic constituent is the union of the qstores of its subconstituents. Part (b) means that each syntactic constituent inherits the cont of its head daughter (this is the main noun in noun phrases, the main verb in verb phrases, and the preposition in prepositional phrases), except for cases where the head daughter combines with an adjunct daughter (a modifier), where the mother syntactic constituent inherits the cont of the adjunct daughter (this case will be discussed further in Section 4.11). Readers familiar with Pollard and Sag’s book (1994) will have noticed that the semantics principle of this book does not allow quantifiers to be unstored from qstore. Apart from this, the principle remains as in Pollard and Sag’s book. The semantics principle causes the qstore of (4.63) to become the union of the qstores of (4.60) and (4.61), i.e., the union of the empty set with a set that contains (4.62). Since the president involves no adjuncts, the ‘semantic head’ is the head daughter i.e., president, and (4.63) inherits the cont of (4.60), which is now the restind of (4.62). The gate 2 of (4.59) is treated as a one-word proper name. In the prototype nlitdb of Chapter 6, the user types multi-word names, like gate 2 and J. Adams,
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as single words. In real-life applications, the words of such names would be concatenated during a preprocessing stage (Section 1.2). Proper names are mapped to signs whose cont is a nom_obj with an empty restr.3 For example, (4.65) shows the lexical sign of gate 2. (4.65)
phon gate2 prd – head noun spr cat subj ss | l comps index gate2 cont {} restr nom_obj qstore {}
The predicative sign of at of (4.51), (4.65), and the predicative sign of was, which is similar to (4.53), except that it introduces a Past operator, cause was at gate 2 in (4.59) to receive (4.66). When was at gate 2 combines with the president, (4.59) receives (4.67), where qstore contains the feature structure of (4.62). According to the semantics principle, the qstore of (4.67) is the union of the qstores of (4.66) and (4.63), and the cont of (4.67) is the same as the cont of (4.66). (4.66)
phon was, at, gate2 vform fin head aux + verb aspect lex_state cat spr subj np -prd 1 ss | l comps tvar + et_handle temp_ent cont arg1 1 main_psoa arg2 gate2 located_at past qstore {}
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From English to TOP
(4.67)
phon the, president, was, at, gate2 vform fin head aux + verb aspect lex_state cat spr subj ss | l comps tvar + et_handle temp_ent cont 1 arg1 main_psoa arg2 gate2 located_at past 3 qstore
The top formula (4.68) is then extracted from (4.67), as discussed in Section 4.6. Whenever an Ntense operator is encountered during the extraction of the top formulae, if there is no definite information showing that the first argument of the Ntense should be now*, the first argument is taken to be a variable. For example, the qstore value of (4.67), shown in (4.62), specifies that the first argument of the Ntense can be either a top variable or now*. Hence, in (4.68) the first argument of the Ntense has become a variable (t v ). During a postprocessing phase, to be discussed in Section 4.17, the Ntense of (4.68) would give rise to two separate formulae: one where the first argument of the Ntense is replaced by now* (current president), and one where the first argument of the Ntense is replaced by the ev of the Past operator (president when at gate 2). In contrast, if the sign shows that the first argument of the Ntense is definitely now*, the first argument of the Ntense in the extracted formula is now*, and the post-processing has no effect on this argument. (4.68) Ntense[t v , president(pv )] ∧ Past[ev , located at(pv , gate2)]
It is possible to force a (non-predicative) noun to be interpreted as referring always to the speech time, or always to the time of the verb tense. (The same mechanism applies to non-predicative adjectives, to be discussed in Section 4.10.) To force a noun to refer always to the speech time, one sets the et_handle of the ntense in the noun’s sign to simply now, instead of allowing it to be either now or a variable-representing index as in (4.60). This way, the et_handle of the ntense in the qstore of (4.67), shown in (4.62),
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would be now. (4.68) would contain now* instead of t v , and the post-processing mechanism would have no effect. To force a noun to refer always to the time of the verb tense, one simply omits the Ntense from the noun’s sign. This would cause the formula extracted from the sign of (4.59) to be (4.69). (4.69) president(pv ) ∧ Past[ev , located at(pv , gate2)]
The semantics of top’s conjunction and Past operator (Sections 3.6 and 3.8, respectively) require president(pv ) and located at(pv , gate2) to be true at the same (past) event time. Hence, (4.69) expresses the reading where the person at gate 2 was the president of that time. There are however, two complications when (non-predicative) noun signs do not introduce Ntense operators. (These also apply to adjective signs.) First, a past perfect sentence like (4.70) receives only (4.71) in the case where the adverbial specifies the reference time. This requires president(pv ) to be true at the time of e1v , i.e., at the reference time, which is required to fall within 1/1/1995. That is, the president is taken to refer to somebody who was the president on 1/1/1995, and who may not have been the president during the visit. (4.70) The president had visited Rome on 1/1/1995. (4.71) president(pv ) ∧ At[1/1/1995, Past[e1v , Perf [e2v , visiting(pv , rome)]]]
In contrast, if the sign of president introduces an Ntense, the formula extracted from the sign of (4.70) is (4.72). The post-processing, then, generates three formulae, corresponding to readings where president refers to the time of the visit (t v replaced by e2v ), the reference time (t v replaced by e1v , equivalent to (4.71)), or the speech time (t v replaced by now*). (4.72) Ntense[t v , president(pv )] ∧ At[1/1/1995, Past[e1v , Perf [e2v , visiting(pv , rome)]]]
The second complication is that (non-predicative) nouns that do not introduce Ntense operators are taken to refer to the time of the main clause’s tense, even if the nouns appear in subordinate clauses. For example, if president does not introduce an Ntense, (4.73) is mapped to (4.74). The semantics of (4.74) requires the visitor to have been president during the building of terminal 2. (4.73) Housecorp built terminal 2 before the president visited terminal 3. (4.74) president(pv ) ∧ Before[Past[e1v , visiting(pv , term3)], Past[e2v , Culm[building(hcorp, term2)]]]
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From English to TOP
In contrast, if president introduces an Ntense, the post-processing generates three readings, where president refers to the speech time, the time of the building, or the time of the visit. The treatment of subordinate clauses will be discussed in Section 4.14. Before moving on to predicative nouns, let us also examine the nonpredicative signs of nouns like day or summer, which refer to members of partitionings (Section 3.4). The signs of these nouns are similar to the nonpredicative signs of ordinary nouns, like president, except that they introduce Part operators and do not introduce Ntense operators. (4.75), for example, shows the non-predicative sign of day. (The day and day_ent_var sorts are as in Figure 4.4 on page 116.) phon day prd – head noun loc | cat | head det cat spr subj comps (4.75) ss | l 1 index day_ent_var partng day cont restr part_var 1 part nom_obj qstore {}
Names of months and days (e.g., Monday, January) that can be used both with and without determiners (e.g., on a Monday, on Monday) receive two nonpredicative signs each: one that requires a determiner, and one that does not. Finally, proper names that refer to particular time-periods (e.g., the year-name 1991 or the date 25/10/1995) receive non-predicative signs that are similar to those of common proper names (e.g., gate 2), except that their index values are subsorts of temp_ent rather than non_temp_ent. Later sections will demonstrate how the signs of temporal nouns and proper names are used to form the signs of temporal adverbials, like for two days, or before 25/10/1995. .. Predicative nouns Let us now examine predicative nouns, like the president of (4.58). (4.76) shows the predicative sign of president. Unlike the signs of non-predicative nouns,
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whose cont values are of sort nom_obj, the cont values of the signs of predicative nouns are of sort psoa (Section 4.3). The president in (4.76) is a subsort of psoa. (4.76)
phon president prd + head noun loc | cat | head det spr cat subj ss | l np -prd 1 comps 1 arg1 person_ent cont president qstore {}
Also, unlike non-predicative nouns that do not require subjects (e.g., (4.60)), predicative nouns do require subjects. In (4.76), president requires a nonpredicative noun phrase as its subject; the 1 stands for the index of that noun phrase. In the hpsg version of this book, the predicative signs of nouns are generated automatically from the non-predicative ones by (4.77); for example, (4.76) is generated from (4.60).4 As with previous lexical rules, features not shown in (4.77) (e.g., spr, comps) have the same values in both the original and the generated signs. The remove ntense( 2 ) in (4.77) means that if 2 , i.e., the element of the restr set in the non-predicative sign is of sort ntense, then the cont of the predicative sign should be the main_psoa of 2 (cf. (4.60)); otherwise, the cont of the predicative sign should be 2 . In other words, if the non-predicative sign introduces an Ntense operator, the operator is removed in the predicative sign. This is in accordance with the observation in Section 2.11 that noun phrases that are complements of to be always refer to the time of the verb tense. For example, (4.78) means that J. Adams was the president in 1992, not at the speech time. (4.78) is represented correctly by (4.79), which does not contain an Ntense operator.
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From English to TOP
(4.77) Predicative Nouns Lexical Rule: ss | l
prd – head cat noun subj index 1 cont 2 restr nom_obj
⇓ prd + head noun cat ss | l subj np -prd 1 cont remove_ntense( 2 )
(4.78) J. Adams was the president in 1992. (4.79) At[1992, Past[ev , president(ja)]]
top predicates introduced by predicative nouns end up within the operators of the tenses of to be; for example, the president(ja) in (4.79) ends up within the Past. This requires the predicates to hold at the times of the tenses. In this book, determiners are also given different signs for their uses in predicative and non-predicative noun phrases.5 For example, apart from (4.61), the determiner the is also given (4.80), where ‘spec|l’ is again an abbreviation of ‘spec|loc’. The spec of (4.80) shows that the sign can only be used with predicative nouns (cf. (4.61)). Unlike determiners of non-predicative noun phrases, determiners of predicative noun phrases have no additional semantic contribution. For example, the ss|l|cont of (4.80) is simply a copy of the cont of the noun, and no quantifier is introduced in qstore (cf. (4.61)).
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Chapter 4 phon the cat (4.80) ss | l cont qstore {}
prd + head noun spr _ cat spec | l _ subj comps 2 cont det spr subj comps 2
head
Going back to (4.58), when the combines with president, the resulting noun phrase receives (4.81). hpsg’s principles, including the semantics principle of (4.64), cause (4.81) to inherit the head, subj, and cont values of (4.76). (4.81)
phon the, president prd + head noun spr cat subj np -prd ss | l 1 comps cont arg1 person_ent 1 president qstore {}
Apart from (4.42) and (4.53), the is auxiliary is also given (4.82), which allows the complement of is to be a predicative noun phrase. (There are similar signs for was.) The 4 s in (4.82) stand for the cont value of the predicative noun phrase.
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From English to TOP
(4.82)
phon is cat ss | l cont qstore {}
vform fin head aux + verb aspect lex_state spr 3 subj comps np subj 3 , prd + : 4 main_psoa 4 pres
(4.82) and (4.81) cause the is the president of (4.58) to receive (4.83). Finally, when is the president combines with J. Adams, (4.58) receives a sign with an empty qstore, whose cont represents (4.84). (4.83)
phon is, the, president vform fin head aux + verb aspect lex_state cat spr ss | l subj np -prd 1 comps
cont main_psoa arg1 president pres qstore {}
person_ent 1
(4.84) Pres[president(ja)]
There are two additional complications with predicative noun phrases. The first one is that in the non-predicative signs of proper names (e.g., (4.65)), the value of restr is the empty set. Hence, (4.77) does not generate the corresponding predicative signs, because the non-predicative signs do not match the restr description of the left-hand side of (4.77), which requires the restr value to be a one-element set. This causes (4.85) to be rejected, because there is no predicative sign for J. Adams. To solve this problem, the additional lexical rule of (4.86) can be used. (4.85) The inspector is J. Adams.
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(4.86) Additional Predicative Nouns Lexical Rule:
prd – head cat noun subj ss | l 1 index cont restr {}
nom_obj
⇓
prd + noun cat subj np -prd 2 ss | l arg1 1 cont 2 arg2
head
identity
This would generate (4.87) from the non-predicative sign of J. Adams; the latter is similar to (4.65). (4.82) and (4.87) would then cause (4.85) to be mapped to (4.88). For simplicity, it is assumed here that the non-predicative inspector does not introduce an Ntense operator (Section 4.9.1). (4.87)
phon J.Adams prd + head noun spr cat subj np -prd 2 ss | l comps arg1 ja cont 2 arg2 identity qstore {}
(4.88) inspector(inspv ) ∧ Pres[identity(ja, inspv )]
The identity(τ1 , τ2 ) is intended to be true at event times where its two arguments denote the same entity. This calls for a special domain-independent semantics for identity(τ1 , τ2 ), an issue that will not be explored further. The second complication is that the non-predicative sign of Monday, which is similar to (4.75), and the treatment of predicative noun phrases above lead to an attempt to map (4.89) to (4.90). (4.89) 23/10/1995 was a Monday.
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From English to TOP
(4.90) Past[ev , Part[mondayg , 23/10/1995]]
(4.90) is problematic for two reasons. First, the past tense of (4.89) is in effect ignored, because the denotation of Part[σ, β] does not depend on lt, which is what the Past operator affects (Sections 3.6 and 3.8). Hence, the implication of (4.89) that 23/10/1995 is a past day is not captured. This problem could be solved by adding the constraint g(β) lt in the semantics of Part[σ, β]. Second, (4.90) violates the syntax of top, which does not allow the second argument of a Part operator to be a constant; this could be solved by enhancing the definition of Part accordingly. Since, sentences like (4.89) are rare in database querying, however, these issues will not be investigated further.
. Adjectives Following Pollard and Sag (1987:64–65), adjectives are also given different signs for their predicative and non-predicative uses. When used as complements of to be, as with closed in (4.91), adjectives are said to be predicative. In all other cases, for example (4.92), adjectives are non-predicative. (4.91) Runway 2 was closed. (4.92) BA737 landed on a closed runway.
Sentence (4.91) is actually ambiguous. The closed may be a predicative adjective or the passive of to close. However, since passives are ignored in this book (Section 2.13), the passive reading of (4.91) will be ignored. In the airport domain, the predicative adjectival sign of closed is (4.93). (4.93)
phon closed prd + head adj spr cat subj ss | l np -prd 1 comps arg1 (gate_ent ∨ runway_ent) 1 cont closed qstore {}
The is and was auxiliaries receive four signs each. One for progressive forms (see (4.42)), one for prepositional phrase complements (see (4.53)), one for
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noun phrase complements (see (4.82)), and one for adjectival complements ((4.94) below). (4.94) and (4.93) cause (4.91) to be mapped to (4.95). phon was vform fin head aux + verb aspect lex_state spr 3 subj cat prd + head (4.94) adj ss | l cat 3 subj comps loc comps 2 cont et_handle tvar + temp_ent cont 2 main_psoa past qstore {}
(4.95) Past[ev , closed(runway2)]
The non-predicative sign of closed in the airport domain is shown in (4.96). The closed in (4.92) is a modifier (adjunct) of runway. The mod|l in (4.96) refers to the synsem|loc (abbreviated as ss|l) of the modified noun. The ss|l|cont of (4.96) is the same as the one of the noun, except that an Ntense is added to the restr of the noun-sign, which requires the entity described by the noun to be closed at some unspecified time. The index of the noun’s sign is also required to represent a gate or runway.
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From English to TOP phon closed prd – head noun _ cat spr head comps mod | l index 1 cat cont restr 2 nom_obj adj spr (4.96) ss | l subj comps 1 index (gate_ent ∨ runway_ent) restr 2 ∪ cont tvar + ∨ now et_handle temp_ent main_psoa arg1 1 closed ntense nom_obj qstore {}
The non-predicative sign of runway in the airport domain is shown in (4.97). It is assumed here that runway does not introduce an Ntense operator (Section 4.9.1). In (4.92), closed combines with runway according to hpsg’s headadjunct schema (Pollard & Sag 1994), leading to (4.98), where 3 is the set of (4.99). (Sets of psoas correspond to conjunctions.) The principles of hpsg cause (4.98) to inherit the head and spr of (4.97). (4.98) also inherits the cont of (4.96), according to the semantics principle of (4.64); in this case, the ‘semantic head’ is the adjunct closed. Then, (4.98), along with the sign of landed, which is the same as (4.1), except that it also introduces Past and Culm operators, and the non-predicative sign of on, which is similar to (4.55), cause (4.92) to be mapped to (4.100). During the post-processing, to be discussed in Section 4.17, (4.100) gives rise to two different formulae, one where t v is replaced by now* (currently closed runway), and one where t v is replaced by ev (closed during the landing).
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Chapter 4 phon runway prd – head noun cat loc | cat | head det spr subj (4.97) ss | l comps index runway_ent 1 cont arg1 1
